Banach空间中的弱非致密性

IF 1 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-08-04 DOI:10.1007/s43034-025-00456-y

Gonzalo García, Gaspar Mora

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引用次数: 0

摘要

本文引入了非致密性弱度（w-DND）的概念。同样地，我们分析了它的主要性质，并证明了w-DND实际上是任何弱非紧性测度的上界。而且，对于弱非紧性的De Blasi测度，这样的上界是尖锐的。作为我们结果的一个应用，我们用w-DND描述了Banach空间的Schur和Dunford-Pettis性质，这使得这个新概念成为泛函分析中的一个有用的工具。

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Weak nondensifiability in Banach spaces

In the present paper, the notion of weak degree of nondensifiability, w-DND, is introduced. Likewise, we analyze its main properties, and we also prove that the w-DND is actually an upper bound for any measure of weak noncompactness. Moreover, for the De Blasi measure of weak noncompactness, such an upper bound is sharp. As an application of our results, we characterize both Schur and Dunford–Pettis properties of a Banach space in terms of the w-DND, which turns out this new concept into a useful tool in functional analysis.

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.