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The Hausdorff measure of noncompactness of matrix operators on some $BK$ spaces. (English) Zbl 1227.47032
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.

47H08Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
46B15Summability and bases in normed spaces
46B45Banach sequence spaces
46B50Compactness in Banach (or normed) spaces
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