{"title":"离散Cesàro空间的对偶Banach空间诱导的fr<s:1>和(LB)序列空间","authors":"J. Bonet, W. Ricker","doi":"10.36045/J.BBMS.200203","DOIUrl":null,"url":null,"abstract":"The Fréchet (resp., (LB)-) sequence spaces ces(p+) := ⋂ r>p ces(r), 1 ≤ p < ∞ (resp. ces(p-) := ⋃ 1<r<p ces(r), 1 < p ≤ ∞), are known to be very different to the classical sequence spaces lp+ (resp., lp). Both of these classes of non-normable spaces ces(p+), ces(p-) are defined via the family of reflexive Banach sequence spaces ces(p), 1 < p < ∞. The dual Banach spaces d(q), 1 < q < ∞, of the discrete Cesàro spaces ces(p), 1 < p < ∞, were studied by G. Bennett, A. Jagers and others. Our aim is to investigate in detail the corresponding sequence spaces d(p+) and d(p-), which have not been considered before. Some of their properties have similarities with those of ces(p+), ces(p-) but, they also exhibit differences. For instance, ces(p+) is isomorphic to a power series Fréchet space of order 1 whereas d(p+) is isomorphic to such a space of infinite order. Every space ces(p+), ces(p-) admits an absolute basis but, none of the spaces d(p+), d(p-) have any absolute basis.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Fréchet and (LB) sequence spaces induced by dual Banach spaces of discrete Cesàro spaces\",\"authors\":\"J. Bonet, W. Ricker\",\"doi\":\"10.36045/J.BBMS.200203\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Fréchet (resp., (LB)-) sequence spaces ces(p+) := ⋂ r>p ces(r), 1 ≤ p < ∞ (resp. ces(p-) := ⋃ 1<r<p ces(r), 1 < p ≤ ∞), are known to be very different to the classical sequence spaces lp+ (resp., lp). Both of these classes of non-normable spaces ces(p+), ces(p-) are defined via the family of reflexive Banach sequence spaces ces(p), 1 < p < ∞. The dual Banach spaces d(q), 1 < q < ∞, of the discrete Cesàro spaces ces(p), 1 < p < ∞, were studied by G. Bennett, A. Jagers and others. Our aim is to investigate in detail the corresponding sequence spaces d(p+) and d(p-), which have not been considered before. Some of their properties have similarities with those of ces(p+), ces(p-) but, they also exhibit differences. For instance, ces(p+) is isomorphic to a power series Fréchet space of order 1 whereas d(p+) is isomorphic to such a space of infinite order. Every space ces(p+), ces(p-) admits an absolute basis but, none of the spaces d(p+), d(p-) have any absolute basis.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.36045/J.BBMS.200203\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.36045/J.BBMS.200203","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
