Measure of noncompactness of operators in Banach spaces

Qinrui SHEN

doi:10.3868/s140-DDD-025-0011-x

Front. Math. China ›› 2025, Vol. 20 ›› Issue (3) : 121 -133. DOI: 10.3868/s140-DDD-025-0011-x

RESEARCH　ARTICLE

Measure of noncompactness of operators in Banach spaces

Qinrui SHEN

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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 $ℓ p (1 ≤ p < ∞)$ . Finally, several common equivalent measures of noncompactness of operators and related proofs are provided.