Hilbert空间中的算子非紧性测度

Abstract

Abstract:

In this paper, by using the classical Hausdorff measure of noncompactess theory, we study the measure of noncompactness of operators in Banach spaces (especially in Hilbert spaces); Specifically, we first give the representation of measure of noncompactness of operators in Banach spaces, and the equivalence of restricted measures in the whole space and subspaces; Finally, we study the equivalent properties of several semi-norms of bounded operator sequences between Hilbert spaces, especially including a kind of operator semi norm generated by Hausdorff measure of noncompactness.

Key words: Measure of noncompactness, Measure of noncompactness of operators, Hilbert space

CLC Number:

O177.92

Shen Qinrui,Sun Junjun. Measure of Non-Compactness of Operators in Hilbert Space[J].Acta mathematica scientia,Series A, 2023, 43(4): 1003-1008.

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Measure of Non-Compactness of Operators in Hilbert Space

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