{"title":"Renorming AM-spaces","authors":"T. Oikhberg, M. Tursi","doi":"10.1090/proc/15714","DOIUrl":null,"url":null,"abstract":"We prove that any separable AM-space $X$ has an equivalent lattice norm for which no non-trivial surjective lattice isometries exist. Moreover, if $X$ has no more than one atom, then this new norm may be an AM-norm. As our main tool, we introduce and investigate the class of so called Benyamini spaces, which ``approximate'' general AM-spaces.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Renorming AM-spaces\",\"authors\":\"T. Oikhberg, M. Tursi\",\"doi\":\"10.1090/proc/15714\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that any separable AM-space $X$ has an equivalent lattice norm for which no non-trivial surjective lattice isometries exist. Moreover, if $X$ has no more than one atom, then this new norm may be an AM-norm. As our main tool, we introduce and investigate the class of so called Benyamini spaces, which ``approximate'' general AM-spaces.\",\"PeriodicalId\":8426,\"journal\":{\"name\":\"arXiv: Functional Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/proc/15714\",\"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: Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/proc/15714","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that any separable AM-space $X$ has an equivalent lattice norm for which no non-trivial surjective lattice isometries exist. Moreover, if $X$ has no more than one atom, then this new norm may be an AM-norm. As our main tool, we introduce and investigate the class of so called Benyamini spaces, which ``approximate'' general AM-spaces.
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