{"title":"八面体性和伽陀平滑性","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":"{\"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}","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}
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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