# Seminario Dottorato: Boundedness and compactness of matrix operators in weighted spaces of sequences

## Wednesday 23 November 2011 - Zhanar Taspaganbetova

ARGOMENTI: Seminari Dottorato

SEMINARIO DOTTORATO
Wednesday 23 November 2011 h. 15:00, room 2BC30
Zhanar Taspaganbetova (University of Astana and Dip. Mat. Padova)
"Boundedness and compactness of matrix operators in weighted spaces of sequences"

-Abstract
One of the main problems in the theory of matrices is to find necessary and sufficient conditions for the elements of a matrix so that the corresponding matrix operator maps continuously one normed space of sequences into another space of sequences. Thus it is very important to find the norm of a matrix operator, or at least, an upper or lower bound for the norm. However, in several spaces, which are very important both theoretically and in the applications, such problems have not been solved yet in full generality for operators corresponding to arbitrary matrices. Therefore, in such spaces researchers have considered some specific classes of matrix operators and have established criteria of boundedness and compactness for operators of such classes.
We prove a new discrete Hardy type inequality involving a kernel which has a more general form than those known in the literature. We obtain necessary and sufficient conditions for the boundedness and compactness of a matrix operator from the weighted $l_{p,v}$ space into the weighted $l_{q,u}$ space defined by $(Af)_j:=sumlimits_{i=j}^infty a_{i,j}f_i$, for all $f={f_i}_{i=1}^{infty} in l_{p,v}$ in case \$1
Rif. int. C. Marastoni, T. Vargiolu