46-XX	Functional analysis {For manifolds modeled on topological linear spaces, see 57N20 , 58Bxx }
46-00	General reference works (handbooks, dictionaries, bibliographies, etc.)
46-01	Instructional exposition (textbooks, tutorial papers, etc.)
46-02	Research exposition (monographs, survey articles)
46-03	Historical {!must also be assigned at least one classification number from section 01}
46-04	Explicit machine computation and programs (not the theory of computation or programming)
46-06	Proceedings, conferences, collections, etc.
46Axx	Topological linear spaces and related structures {For function spaces, see 46Exx }
46A03	General theory of locally convex spaces
46A04	Locally convex Fr\'echet spaces and (DF)-spaces
46A08	Barrelled spaces, bornological spaces
46A11	Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A13	Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40 ]
46A16	Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46A17	Bornologies and related structures; Mackey convergence, etc.
46A19	Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\bf R}$, etc.)
46A20	Duality theory
46A22	Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10 ]
46A25	Reflexivity and semi-reflexivity [See also 46B10 ]
46A30	Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
46A32	Spaces of linear operators; topological tensor products; approximation properties [See also 46B28 , 46M05 , 47L05 , 47L20 ]
46A35	Summability and bases [See also 46B15 ]
46A40	Ordered topological linear spaces, vector lattices [See also 06F20 , 46B40 , 46B42 ]
46A45	Sequence spaces (including K\"othe sequence spaces) [See also 46B45 ]
46A50	Compactness in topological linear spaces; angelic spaces, etc.
46A55	Convex sets in topological linear spaces; Choquet theory [See also 52A07 ]
46A61	Graded Fr\'echet spaces and tame operators
46A63	Topological invariants ((DN), ($\Omega$), etc.)
46A70	Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
46A80	Modular spaces
46A99	None of the above, but in this section
46Bxx	Normed linear spaces and Banach spaces; Banach lattices {For function spaces, see 46Exx }
46B03	Isomorphic theory (including renorming) of Banach spaces
46B04	Isometric theory of Banach spaces
46B07	Local theory of Banach spaces
46B08	Ultraproduct techniques in Banach space theory [See also 46M07 ]
46B09	Probabilistic methods in Banach space theory [See also 60Bxx ]
46B10	Duality and reflexivity [See also 46A25 ]
46B15	Summability and bases [See also 46A35 ]
46B20	Geometry and structure of normed linear spaces
46B22	Radon-Nikodym, Kreuin-Milman and related properties [See also 46G10 ]
46B25	Classical Banach spaces in the general theory
46B26	Nonseparable Banach spaces
46B28	Spaces of operators; tensor products; approximation properties [See also 46A32 , 46M05 , 47L05 , 47L20 ]
46B40	Ordered normed spaces [See also 46A40 , 46B42 ]
46B42	Banach lattices [See also 46A40 , 46B40 ]
46B45	Banach sequence spaces [See also 46A45 ]
46B50	Compactness in Banach (or normed) spaces
46B70	Interpolation between normed linear spaces [See also 46M35 ]
46B99	None of the above, but in this section
46Cxx	Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx }
46C05	Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46C07	Hilbert subspaces; complementation (Aronszajn, de_Branges, ...) [See 46B70 , 46M35 ]
46C15	Characterizations of Hilbert spaces
46C20	Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, ...)
46C50	Generalizations of inner products (semi-inner products, partial inner products, etc.)
46C99	None of the above, but in this section
46Exx	Linear function spaces and their duals [See also 30H05 , 32A38 , 46F05 ] {For function algebras, see 46J10 }
46E05	Lattices of continuous, differentiable or analytic functions
46E10	Topological linear spaces of continuous, differentiable or analytic functions
46E15	Banach spaces of continuous, differentiable or analytic functions
46E20	Hilbert spaces of continuous, differentiable or analytic functions
46E22	Hilbert spaces with reproducing kernels (= [Proper] functional Hilbert spaces)
46E25	Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10 , 46J15 }
46E27	Spaces of measures [See also 28A33 , 46Gxx ]
46E30	Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35	Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
46E39	Sobolev (and similar kinds of) spaces of functions of discrete variables
46E40	Spaces of vector- and operator-valued functions
46E50	Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20 , 46G25 , 47H60 ]
46E99	None of the above, but in this section
46Fxx	Distributions, generalized functions, distribution spaces [See also 46T30 ]
46F05	Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10 , 46E35 ]
46F10	Operations with distributions
46F12	Integral transforms in distribution spaces [See also 42-XX , 44-XX ]
46F15	Hyperfunctions, analytic functionals [See also 32A25 , 32A45 , 32C35 , 58J15 ]
46F20	Distributions and ultradistributions as boundary values of analytic functions [See also 30D40 , 30E25 , 32A40 ]
46F25	Distributions on infinite-dimensional spaces [See also 58C35 ]
46F30	Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
46F99	None of the above, but in this section
46Gxx	Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX , 46Txx ]
46G05	Derivatives [See also 46T20 , 58C20 , 58C25 ]
46G10	Vector-valued measures and integration [See also 28Bxx , 46B22 ]
46G12	Measures and integration on abstract linear spaces [See also 28C20 , 46T12 ]
46G15	Functional analytic lifting theory [See also 28A51 ]
46G20	Infinite-dimensional holomorphy [See also 32-XX , 46E50 , 46T25 58B12 , 58C10 ]
46G25	(Spaces of) multilinear mappings, polynomials [See also 46E50 , 46G20 , 47H60 ]
46G99	None of the above, but in this section
46Hxx	Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10 , 43A20 }
46H05	General theory of topological algebras
46H10	Ideals and subalgebras
46H15	Representations of topological algebras
46H20	Structure, classification of topological algebras
46H25	Normed modules and Banach modules, topological modules {!if not placed in 13-XX or 16-XX }
46H30	Functional calculus in topological algebras [See also 47A60 ]
46H35	Topological algebras of operators [See mainly 47Lxx ]
46H40	Automatic continuity
46H70	Nonassociative topological algebras [See also 46K70 , 46L70 ]
46H99	None of the above, but in this section
46Jxx	Commutative Banach algebras and commutative topological algebras [See also 46E25 ]
46J05	General theory of commutative topological algebras
46J10	Banach algebras of continuous functions, function algebras [See also 46E25 ]
46J15	Banach algebras of differentiable or analytic functions, $H^p$-spaces [See also 30D55 , 30H05 , 32A35 , 32A37 , 32A38 , 42B30 ]
46J20	Ideals, maximal ideals, boundaries
46J25	Representations of commutative topological algebras
46J30	Subalgebras
46J40	Structure, classification of commutative topological algebras
46J45	Radical Banach algebras
46J99	None of the above, but in this section
46Kxx	Topological (rings and) algebras with an involution [See also 16W10 ]
46K05	General theory of topological algebras with involution
46K10	Representations of topological algebras with involution
46K15	Hilbert algebras
46K50	Nonselfadjoint (sub)algebras in algebras with involution
46K70	Nonassociative topological algebras with an involution [See also 46H70 , 46L70 ]
46K99	None of the above, but in this section
46Lxx	Selfadjoint operator algebras ($C^*$-algebras, von_Neumann ($W^*$-) algebras, etc.) [See also 22D25 ]
46L05	General theory of $C^*$-algebras
46L06	Tensor products of $C^*$-algebras; free products of $C^*$-algebras
46L07	Operator spaces and completely bounded map [See also 47L25 ]
46L08	$C^*$-modules
46L10	General theory of von_Neumann algebras
46L30	States
46L35	Classifications of $C^*$-algebras, factors
46L37	Subfactors and their classification
46L40	Automorphisms
46L45	Decomposition theory for $C^*$-algebras
46L51	Noncommutative measure and integration
46L52	Noncommutative function spaces
46L53	Noncommutative probability and statistics
46L54	Free probability and free operator algebras
46L55	Noncommutative dynamical systems [See also 28Dxx , 54H20 , 37Kxx , 37Lxx ]
46L57	Derivations, dissipations and positive semigroups in $C^*$-algebras
46L60	Applications of selfadjoint operator algebras to physics [See also 46N50 , 46N55 , 47L90 , 81T05 , 82B10 , 82C10 ]
46L65	Quantizations, deformations
46L70	Nonassociative selfadjoint operator algebras [See also 46H70 , 46K70 ]
46L80	$K$-theory and operator algebras (including cyclic theory) [See also 18F25 , 19Kxx , 46M20 , 55Rxx , 58J22 ]
46L85	Noncommutative topology [See also 58B32 , 58B34 , 58J22 ]
46L87	Noncommutative differential geometry [See also 58B32 , 58B34 , 58J22 ]
46L89	Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32 , 58B34 , 58J22 ]
46L99	None of the above, but in this section
46Mxx	Methods of category theory in functional analysis [See also 18-XX ]
46M05	Tensor products [See also 46A32 , 46B28 , 47A80 ]
46M07	Ultraproducts [See also 46B08 , 46S20 ]
46M10	Projective and injective objects [See also 46A22 ]
46M15	Categories, functors {For $K$-theory, EXT, etc., see 19K33 , 46L80 , 46M18 , 46M20 }
46M18	Homological methods (exact sequences, right inverses, lifting, etc.,)
46M20	Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05 , 18Fxx , 19Kxx , 32Cxx , 32Lxx , 46L80 , 46M15 , 46M18 , 55Rxx ]
46M35	Abstract interpolation of topological vector spaces [See also 46B70 ]
46M40	Inductive and projective limits [See also 46A13 ]
46M99	None of the above, but in this section
46Nxx	Miscellaneous applications of functional analysis [See also 47Nxx ]
46N10	Applications in optimization, convex analysis, mathematical programming, economics
46N20	Applications to differential and integral equations
46N30	Applications in probability theory and statistics
46N40	Applications in numerical analysis [See also 65Jxx ]
46N50	Applications in quantum physics
46N55	Applications in statistical physics
46N60	Applications in biology and other sciences
46N99	None of the above, but in this section
46Sxx	Other (nonclassical) types of functional analysis [See also 47Sxx ]
46S10	Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis [See also 12J25 , 32P05 ]
46S20	Nonstandard functional analysis [See also 03H05 ]
46S30	Constructive functional analysis [See also 03F60 ]
46S40	Fuzzy functional analysis [See also 03E72 ]
46S50	Functional analysis in probabilistic metric linear spaces
46S60	Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50 ]
46S99	None of the above, but in this section
46Txx	Nonlinear functional analysis [See also 47Hxx , 47Jxx , 58Cxx , 58Dxx ]
46T05	Infinite-dimensional manifolds [See also 53Axx , 58Bxx , 58Dxx , 57N20 ]
46T10	Manifolds of mappings
46T12	Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx , 46G12 , 60-XX ]
46T20	Continuous and differentiable maps [See also 46G05 ]
46T25	Holomorphic maps [See also 46G20 ]
46T30	Distribution and generalized functions on nonlinear spaces [See also 46Fxx ]
46T99	None of the above, but in this section