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

被引：2

作者：

Kaczor, Wieslawa ^{[1
]}

Kuczumow, Tadeusz ^{[1
]}

Reich, Simeon ^{[2
]}

Walczyk, Mariola ^{[3
]}

机构：

[1] UMCS, Inst Matemat, PL-20031 Lublin, Poland

[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[3] Rzeszow Tech Univ, Wydzial Matemat & Fizyki Stosowanej, PL-35959 Rzeszow, Poland

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2021年 / 25卷 / 04期

基金：

以色列科学基金会;

关键词：

Day norm; diametrically complete set; Kadec-Klee property; LUR; nonstrict Opial property; reflexive Banach space;

D O I：

10.11650/tjm/201205

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：743 / 755

页数：13

共 30 条

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