A note on compact operators on matrix domains

We establish some identities or estimates for the operator norms and Hausdorff measures of noncompactness of linear operators given by infinite matrices that map the matrix domains of triangles in arbitrary BK spaces with AK, or in the spaces of all convergent or bounded sequences, into the spaces o...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-04, Vol.340 (1), p.291-303
Main Authors: Djolović, Ivana, Malkowsky, Eberhard
Format: Article
Language:English
Subjects:
BK and AK spaces
Compact operators
Exact sciences and technology
Mathematical analysis
Mathematics
Matrix domains
Matrix transformations
Measure of noncompactness
Operator theory
Sciences and techniques of general use
Sequence spaces
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We establish some identities or estimates for the operator norms and Hausdorff measures of noncompactness of linear operators given by infinite matrices that map the matrix domains of triangles in arbitrary BK spaces with AK, or in the spaces of all convergent or bounded sequences, into the spaces of all null, convergent or bounded sequences, or of all absolutely convergent series. Furthermore, we apply these results to the characterizations of compact operators on the matrix domains of triangles in the classical sequence spaces, and on the sequence spaces studied in [I. Djolović, Compact operators on the spaces a 0 r ( Δ ) and a c r ( Δ ) , J. Math. Anal. Appl. 318 (2) (2006) 658–666; I. Djolović, On the space of bounded Euler difference sequences and some classes of compact operators, Appl. Math. Comput. 182 (2) (2006) 1803–1811].
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.08.021