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2021 Renormings of Nonseparable Reflexive Banach Spaces and Diametrically Complete Sets with Empty Interior
Wiesława Kaczor, Tadeusz Kuczumow, Simeon Reich, Mariola Walczyk
Taiwanese J. Math. Advance Publication 1-13 (2021). DOI: 10.11650/tjm/201205

Abstract

We prove that for each nonseparable and reflexive Banach space $(X,\|\cdot\|_X)$ with the nonstrict Opial and Kadec--Klee properties, there exists an equivalent norm $\|\cdot\|_0$ such that the Banach space $(X,\|\cdot\|_0)$ is LUR and contains a diametrically complete set with empty interior.

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Wiesława Kaczor. Tadeusz Kuczumow. Simeon Reich. Mariola Walczyk. "Renormings of Nonseparable Reflexive Banach Spaces and Diametrically Complete Sets with Empty Interior." Taiwanese J. Math. Advance Publication 1 - 13, 2021. https://doi.org/10.11650/tjm/201205

Information

Published: 2021
First available in Project Euclid: 18 December 2020

Digital Object Identifier: 10.11650/tjm/201205

Subjects:
Primary: 46G20, 52A05

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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