{"title":"Banach limit in convexity and geometric means for convex bodies","authors":"Liran Rotem","doi":"10.3934/ERA.2016.23.005","DOIUrl":null,"url":null,"abstract":"In this note we construct Banach limits on the class of sequences \nof convex bodies. Surprisingly, the construction uses the recently \nintroduced geometric mean of convex bodies. In the opposite direction, \nwe explain how Banach limits can be used to construct a new variant \nof the geometric mean that has some desirable properties.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"23 1","pages":"41-51"},"PeriodicalIF":0.0000,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Research Announcements in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/ERA.2016.23.005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 6
Abstract
In this note we construct Banach limits on the class of sequences
of convex bodies. Surprisingly, the construction uses the recently
introduced geometric mean of convex bodies. In the opposite direction,
we explain how Banach limits can be used to construct a new variant
of the geometric mean that has some desirable properties.
期刊介绍：
Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication.
ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007
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