不可分离自反Banach空间与内部空的直径完全集合的改造

IF 0.6 4区数学 Q3 MATHEMATICS

Taiwanese Journal of Mathematics Pub Date : 2021-01-01 DOI:10.11650/tjm/201205

W. Kaczor, T. Kuczumow, S. Reich, Mariola Walczyk

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引用次数: 2

摘要

证明了对于每一个具有非严格Opial和Kadec-Klee性质的不可分自反的Banach空间(X，‖·‖X)，存在一个等价范数‖·‖0，使得该Banach空间(X，‖·‖0)是LUR且包含一个内部空的径完全集合。

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Renormings of Nonseparable Reflexive Banach Spaces and Diametrically Complete Sets with Empty Interior

We prove that for each nonseparable and reflexive Banach space (X, ‖ · ‖X) with the nonstrict Opial and Kadec–Klee properties, there exists an equivalent norm ‖ · ‖0 such that the Banach space (X, ‖ · ‖0) is LUR and contains a diametrically complete set with empty interior.

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来源期刊

Taiwanese Journal of Mathematics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： The Taiwanese Journal of Mathematics, published by the Mathematical Society of the Republic of China (Taiwan), is a continuation of the former Chinese Journal of Mathematics (1973-1996). It aims to publish original research papers and survey articles in all areas of mathematics. It will also occasionally publish proceedings of conferences co-organized by the Society. The purpose is to reflect the progress of the mathematical research in Taiwan and, by providing an international forum, to stimulate its further developments. The journal appears bimonthly each year beginning from 2008.