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Zbl 1227.47032
Mursaleen, M.; Noman, Abdullah K.
The Hausdorff measure of noncompactness of matrix operators on some $BK$ spaces.
(English)
[J] Oper. Matrices 5, No. 3, 473-486 (2011). ISSN 1846-3886

Summary: We establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the spaces $c^\lambda_0$ and $\ell^\lambda_\infty$which have recently been introduced in [{\it M. Mursaleen} and {\it A. K. Noman}, On the spaces of $\lambda$-convergent and bounded sequences'', Thai J. Math. 8, No.~2, 311--329 (2010; Zbl 1218.46005)]. Further, by using the Hausdorff measure of noncompactness, we characterize some classes of compact operators on these spaces.
MSC 2000:
*47H08
46B15 Summability and bases in normed spaces
46B45 Banach sequence spaces
46B50 Compactness in normed spaces

Keywords: BK space; matrix transformation; compact operator; Hausdorff measure of noncompactness

Citations: Zbl 1218.46005

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