{"title":"关于弱$^*$导集是适当且范数稠密的子空间","authors":"Zdenvek Silber","doi":"10.4064/sm220303-29-4","DOIUrl":null,"url":null,"abstract":"We study long chains of iterated weak∗ derived sets, that is sets of all weak∗ limits of bounded nets, of subspaces with the additional property that the penultimate weak∗ derived set is a proper norm dense subspace of the dual. We extend the result of Ostrovskii and show, that in the dual of any nonquasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual, we can find for any countable successor ordinal α a subspace, whose weak∗ derived set of order α is proper and norm dense.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On subspaces whose weak$^*$ derived sets are proper and norm dense\",\"authors\":\"Zdenvek Silber\",\"doi\":\"10.4064/sm220303-29-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study long chains of iterated weak∗ derived sets, that is sets of all weak∗ limits of bounded nets, of subspaces with the additional property that the penultimate weak∗ derived set is a proper norm dense subspace of the dual. We extend the result of Ostrovskii and show, that in the dual of any nonquasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual, we can find for any countable successor ordinal α a subspace, whose weak∗ derived set of order α is proper and norm dense.\",\"PeriodicalId\":51179,\"journal\":{\"name\":\"Studia Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/sm220303-29-4\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm220303-29-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On subspaces whose weak$^*$ derived sets are proper and norm dense
We study long chains of iterated weak∗ derived sets, that is sets of all weak∗ limits of bounded nets, of subspaces with the additional property that the penultimate weak∗ derived set is a proper norm dense subspace of the dual. We extend the result of Ostrovskii and show, that in the dual of any nonquasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual, we can find for any countable successor ordinal α a subspace, whose weak∗ derived set of order α is proper and norm dense.
期刊介绍:
The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.