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August, 2021 Renormings of Nonseparable Reflexive Banach Spaces and Diametrically Complete Sets with Empty Interior
Wiesława Kaczor, Tadeusz Kuczumow, Simeon Reich, Mariola Walczyk
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Taiwanese J. Math. 25(4): 743-755 (August, 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.

Funding Statement

The third author was partially supported by the Israel Science Foundation (Grant Nos. 389/12 and 820/17), the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund.

Acknowledgments

All the authors are grateful to two anonymous referees for their useful comments and helpful suggestions.

Citation

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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. 25 (4) 743 - 755, August, 2021. https://doi.org/10.11650/tjm/201205

Information

Received: 17 March 2020; Revised: 5 October 2020; Accepted: 10 December 2020; Published: August, 2021
First available in Project Euclid: 18 December 2020

Digital Object Identifier: 10.11650/tjm/201205

Subjects:
Primary: 46G20 , 52A05

Keywords: Day norm , diametrically complete set , Kadec–Klee property , LUR , nonstrict Opial property , reflexive Banach space

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

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Vol.25 • No. 4 • August, 2021
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