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
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
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