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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 2

Issues

Matrix mappings and general bounded linear operators on the space bv

Ivana Djolović / Katarina Petković / Eberhard Malkowsky
Published Online: 2018-03-31 | DOI: https://doi.org/10.1515/ms-2017-0111

Abstract

If X and Y are FK spaces, then every infinite matrix A ∈ (X, Y) defines a bounded linear operator LAB(X, Y) where LA(x) = Ax for each xX. But the converse is not always true. Indeed, if L is a general bounded linear operator from X to Y, that is, LB(X, Y), we are interested in the representation of such an operator using some infinite matrices. In this paper we establish the representations of the general bounded linear operators from the space bv into the spaces , c and c0. We also prove some estimates for their Hausdorff measures of noncompactness. In this way we show the difference between general bounded linear operators between some sequence spaces and the matrix operators associated with matrix transformations.

MSC 2010: Primary 46B45; Secondary 47B37

Keywords: BK spaces; sequences of bounded variation; matrix mappings; bounded and compact linear operators

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About the article

Research of the first and the third author supported by the research project #174007 and #174025, respectively, of the Serbian Ministry of Science, Technology and Environmental Development, and of the third author also by the project #114F104 of Tubitak.

*1

Received: 2016-03-11

Accepted: 2016-05-23

Published Online: 2018-03-31

Published in Print: 2018-04-25


Citation Information: Mathematica Slovaca, Volume 68, Issue 2, Pages 405–414, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0111.

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