Fernando Albiac, Jose L. Ansorena, Pablo Berná, Miguel Berasategui
{"title":"带属性的条件基~(A)","authors":"Fernando Albiac, Jose L. Ansorena, Pablo Berná, Miguel Berasategui","doi":"arxiv-2409.04883","DOIUrl":null,"url":null,"abstract":"Property~(A) is a week symmetry condition that plays a fundamental role in\nthe characterization of greedy-type bases in the isometric case, i.e., when the\nconstants involved in the study of the efficiency of the thresholding greedy\nalgorithm in Banach spaces are sharp. In this note we build examples of Banach\nspaces with Schauder bases that have Property~(A) but fail to be unconditional,\nthus settling a long standing problem in the area. As a by-product of our work\nwe hone our construction to produce counterexamples that solve other open\nquestions in the isometric theory of greedy bases.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"252 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Conditional bases with Property~(A)\",\"authors\":\"Fernando Albiac, Jose L. Ansorena, Pablo Berná, Miguel Berasategui\",\"doi\":\"arxiv-2409.04883\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Property~(A) is a week symmetry condition that plays a fundamental role in\\nthe characterization of greedy-type bases in the isometric case, i.e., when the\\nconstants involved in the study of the efficiency of the thresholding greedy\\nalgorithm in Banach spaces are sharp. In this note we build examples of Banach\\nspaces with Schauder bases that have Property~(A) but fail to be unconditional,\\nthus settling a long standing problem in the area. As a by-product of our work\\nwe hone our construction to produce counterexamples that solve other open\\nquestions in the isometric theory of greedy bases.\",\"PeriodicalId\":501036,\"journal\":{\"name\":\"arXiv - MATH - Functional Analysis\",\"volume\":\"252 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-07\",\"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-2409.04883\",\"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-2409.04883","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Property~(A) is a week symmetry condition that plays a fundamental role in
the characterization of greedy-type bases in the isometric case, i.e., when the
constants involved in the study of the efficiency of the thresholding greedy
algorithm in Banach spaces are sharp. In this note we build examples of Banach
spaces with Schauder bases that have Property~(A) but fail to be unconditional,
thus settling a long standing problem in the area. As a by-product of our work
we hone our construction to produce counterexamples that solve other open
questions in the isometric theory of greedy bases.
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