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Matrix Mappings and General Bounded Linear Operators on the Space Bv by Ivana Djolović; Katarina Petković; Eberhard Malkowsky is a Mathematics article available to read on EtoBox.

What is Matrix Mappings and General Bounded Linear Operators on the Space Bv about?

If X and Y are F K spaces, then every infinite matrix A ∈ (X, Y ) defines a bounded linear operator L A ∈ B(X, Y ) where L A (x) = Ax for each x ∈ X. But the converse is not always true. Indeed, if L is a general bounded linear operator from X to Y , that is, L ∈ B(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 c 0 . 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.

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Author

Ivana Djolović; Katarina Petković; Eberhard Malkowsky

Publisher

SP Versita; De Gruyter Open Sp. z o.o. ; Walter de Gruyter GmbH (ISSN 0139-9918)

Published

2018

Language

EN

Field

Mathematics (Physical Sciences)