Measure of noncompactness of operators in Banach spaces

Abstract

This paper is committed to dealing with the measure of noncompactness of operators in Banach spaces. First, we give a characterization of the measure of noncompact Hausdorff operators with respect to the Hausdorff metric. Then, we show a formula of the Hausdorff measure of noncompactness of operators in . Finally, several common equivalent measures of noncompactness of operators and related proofs are provided.

Keywords

Measure of noncompactness / measure of noncompactness of operators / equivalent measure / Banach space

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