{"title":"Octahedrality and Gâteaux smoothness","authors":"Ch. Cobollo, P. Hájek","doi":"arxiv-2408.03737","DOIUrl":null,"url":null,"abstract":"We prove that every Banach space admitting a Gateaux smooth norm and\ncontaining a complemented copy of $\\ell_1$ has an equivalent renorming which is\nsimultaneously G\\^ateaux smooth and octahedral. This is a partial solution to a\nproblem from the early nineties.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"194 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03737","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that every Banach space admitting a Gateaux smooth norm and
containing a complemented copy of $\ell_1$ has an equivalent renorming which is
simultaneously G\^ateaux smooth and octahedral. This is a partial solution to a
problem from the early nineties.
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