47-XX 
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Operator theory
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47-00
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General reference works (handbooks, dictionaries, bibliographies, etc.)
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47-01
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Instructional exposition (textbooks, tutorial papers, etc.)
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47-02
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Research exposition (monographs, survey articles)
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47-03
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Historical {!must also be assigned at least one classification number from section 01}
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47-04
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Explicit machine computation and programs (not the theory of computation or programming)
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47-06
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Proceedings, conferences, collections, etc.
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47Axx
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General theory of linear operators
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47A05
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General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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47A06
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Linear relations (multivalued linear operators)
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47A07
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Forms (blilinear, sesquilinear, multilinear)
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47A10
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Spectrum, resolvent
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47A11
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Local spectral properties
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47A12
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Numerical range, numerical radius
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47A13
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Several-variable operator theory (spectral, Fredholm, etc.)
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47A15
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Invariant subspaces
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47A16
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Cyclic and hypercyclic vectors
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47A20
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Dilations, extensions, compressions
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47A25
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Spectral sets
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47A30
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Norms (inequalities, more than one norm, etc.)
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47A35
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Ergodic theory
[See also
37Axx ]
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47A40
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Scattering theory
[See also
34L25 ,
35P25 ,
81Uxx ]
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47A45
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Canonical models for contractions and nonselfadjoint operators
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47A46
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Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
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47A48
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Operator colligations (=nodes), vessels, linear systems, characteristic functions, realizations, etc.
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47A50
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Equations and inequalities involving linear operators, with vector unknowns
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47A53
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(Semi-) Fredholm operators; index theories
[See also
58B10 ,
58J20 ]
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47A55
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Perturbation theory
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47A56
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Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
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47A57
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Operator methods in interpolation, moment and extension problems
[See also
30E05 ,
42A70 ,
42A82 ,
44A60 ]
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47A58
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Operator approximation theory
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47A60
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Functional calculus
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47A62
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Equations involving linear operators, with operator unknowns
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47A63
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Operator inequalities
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47A64
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Operator means, shorted operators, etc.
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47A65
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Structure theory
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47A66
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Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
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47A67
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Representation theory
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47A68
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Factorization theory (including Wiener-Hopf and spectral factorizations)
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47A70
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(Generalized) eigenfunction expansions; rigged Hilbert spaces
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47A75
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Eigenvalue problems
[See also
49R50 ]
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47A80
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Tensor products of operators
[See also
46M05 ]
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47A99
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None of the above, but in this section
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47Bxx
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Special classes of linear operators
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47B06
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Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc.
Of operators
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47B07
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Operators defined by compactness properties
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47B10
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Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von_Neumann classes, etc.)
[See also
47L20 ]
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47B15
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Hermitian and normal operators (spectral measures, functional calculus, etc.)
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47B20
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Subnormal operators, hyponormal operators, etc.
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47B25
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Symmetric and selfadjoint operators (unbounded)
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47B32
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Operators in reproducing-kernel Hilbert spaces
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47B33
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Composition operators
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47B34
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Kernel operators
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47B35
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Toeplitz operators, Hankel operators, Wiener-Hopf operators
{For other integral operators, see also
45P05 ,
47G10 }
[See also
32A25 ,
32M15 ]
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47B36
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Jacobi (tridiagonal) operators (matrices) and generalizations
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47B37
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Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
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47B38
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Operators on function spaces (general)
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47B39
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Difference operators
[See also
39A70 ]
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47B40
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Spectral operators, decomposable operators, well-bounded operators, etc.
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47B44
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Accretive operators, dissipative operators, etc.
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47B47
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Commutators, derivations, elementary operators, etc.
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47B48
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Operators on Banach algebras
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47B49
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Transformers (=operators on spaces of operators)
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47B50
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Operators on spaces with an indefinite metric
[See also
46C50 ]
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47B60
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Operators on ordered spaces
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47B65
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Positive operators and order-bounded operators
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47B80
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Random operators
[See also
60H25 ]
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47B99
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None of the above, but in this section
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47Cxx
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Individual linear operators as elements of algebraic systems
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47C05
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Operators in algebras
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47C10
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Operators in *-algebras
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47C15
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Operators in $C^*$- or von_Neumann algebras
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47C99
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None of the above, but in this section
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47Dxx
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Groups and semigroups of linear operators, their generalizations and applications
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47D03
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Groups and semigroups of linear operators
{For nonlinear operators, see
47H20 }
[See also
20M20 ]
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47D06
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One-parameter semigroups and linear evolution equations
[See also
34G10 ,
34K30 ]
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47D07
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Markov semigroups and applications to diffusion processes
{For Markov processes, see
60Jxx }
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47D08
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Schr\"odinger and Feynman-Kac semigroups
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47D09
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Operator sine and cosine functions and higher-order Cauchy problems
[See also
34G10 ]
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47D60
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$C$-semigroups
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47D62
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Integrated semigroups
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47D99
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None of the above, but in this section
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47E05
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Ordinary differential operators
[See also
34Bxx ,
34Lxx ]
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47F05
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Partial differential operators
[See also
35Pxx ,
58Jxx ]
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47Gxx
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Integral, integro-differential, and pseudodifferential operators
[See also
58Jxx ]
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47G10
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Integral operators
[See also
45P05 ]
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47G20
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Integro-differential operators
[See also
34K30 ,
35R10 ,
45J05 ,
45K05 ]
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47G30
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Pseudodifferential operators
[See also
35Sxx ,
58Jxx ]
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47G99
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None of the above, but in this section
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47Hxx
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Nonlinear operators and their properties
{For global and geometric aspects, see
58-XX ,
especially
58Cxx }
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47H04
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Set-valued operators
[See also
28B20 ,
54C60 ,
58C06 ]
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47H05
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Monotone operators (with respect to duality)
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47H06
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Accretive operators, dissipative operators, etc.
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47H07
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Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
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47H09
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Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, $A$-proper mappings, $K$-set contractions, etc.)
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47H10
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Fixed-point theorems
[See also
54H25 ,
55M20 ,
58C30 ]
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47H11
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Degree theory
[See also
55M25 ,
58C30 ]
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47H12
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Spectral theory of nonlinear operators
[See also
58C40 ]
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47H14
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Perturbations of nonlinear operators
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47H20
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Semigroups of nonlinear operators
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47H30
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Particular nonlinear operators (superposition, Hammerstein, Nemytski\u i, Uryson, etc.)
[See also
45P05 ]
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47H40
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Random operators
[See also
60H25 ]
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47H50
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Potential operators
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47H60
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Multilinear and polynomial operators
[See also
46G25 ]
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47H99
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None of the above, but in this section
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47Jxx
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Equations and inequalities involving linear operators
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47J05
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Equations involving nonlinear operators (general)
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47J07
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Abstract inverse mapping and implicit function theorems
[See also
46T20
and
58C15 ]
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47J10
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Nonlinear eigenvalue problems
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47J15
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Abstract bifurcation theory
[See also
58E07 ,
58E09 ]
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47J20
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Variational and other type of inequalities involving nonlinear operators (general)
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47J25
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Methods for solving nonlinear operator equations (general)
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47J30
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Infinite-dimensional critical point theory and variational methods
[See also
58Exx ]
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47J35
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Nonlinear evolution equations
[See also
34G20 ,
35K90 ,
35L90 ,
35Qxx ,
35R20 ,
47H20 ,
58D25 ]
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47J40
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Equations with hysteresis
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47J99
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None of the above, but in this section
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47Lxx
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Linear spaces and algebras of operators
[See also
46Lxx ]
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47L05
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Linear spaces of operators
[See also
46A32
and
46B28 ]
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47L07
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Convex sets and cones of operators
[See also
46A55 ,
90C25 ,
and
90C31 ]
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47L10
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Algebras of operators on Banach spaces and other topological linear spaces
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47L15
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Operator algebras with symbol structure
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47L20
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Operator ideals
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47L25
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Operator spaces (=matricially normed spaces)
[See also
46L07 ]
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47L30
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Abstract operator algebras on Hilbert spaces
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47L35
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Nest algebras, CSL algebras
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47L40
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Limit algebras, subalgebras of $C^*$-algebras
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47L45
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Dual algebras; weakly closed singly generated operator algebras
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47L50
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Dual spaces of operator algebras
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47L55
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Representations of (nonselfadjoint) operator algebras
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47L60
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Algebras of unbounded operators; partial algebras of operators
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47L65
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Crossed product algebras (analytic crossed products)
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47L70
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Nonassociative nonselfadjoint operator algebras
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47L75
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Other nonselfadjoint operator algebras
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47L80
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Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
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47L90
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Applications of operator algebras to physics
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47L99
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None of the above, but in this section
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47Nxx
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Miscellaneous applications of operator theory
[See also
46Nxx ]
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47N10
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Applications in optimization, convex analysis, mathematical programming, economics
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47N20
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Applications to differential and integral equations
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47N30
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Applications in probability theory and statistics
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47N40
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Applications in numerical analysis
[See also
65Jxx ]
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47N50
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Applications in quantum physics
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47N55
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Applications in statistical physics
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47N60
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Applications in biology and other sciences
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47N70
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Applications in systems theory, circuits, etc.
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47N99
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None of the above, but in this section
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47Sxx
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Other (nonclassical) types of operator theory
[See also
46Sxx ]
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47S10
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Operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory
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47S20
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Nonstandard operator theory
[See also
03H05 ]
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47S30
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Constructive operator theory
[See also
03F65 ]
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47S40
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Fuzzy operator theory
[See also
03E72 ]
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47S50
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Operator theory in probabilistic metric linear spaces
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47S99
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None of the above, but in this section
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