{"title":"Renormings of Nonseparable Reflexive Banach Spaces and Diametrically Complete Sets with Empty Interior","authors":"W. Kaczor, T. Kuczumow, S. Reich, Mariola Walczyk","doi":"10.11650/tjm/201205","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Taiwanese Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.11650/tjm/201205","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
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.
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.
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