{"title":"I- 内积空间子空间序列的收敛性","authors":"Prasanta Malik, Saikat Das","doi":"10.56947/gjom.v17i1.2082","DOIUrl":null,"url":null,"abstract":"In this paper we introduce the notion of ℑ-convergence of sequences of k-dimensional subspaces of an inner product space, where ℑ is an ideal of subsets of ℕ, the set of all natural numbers and k⊂ℕ. We also study some basic properties of this notion.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"51 6","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"I- Convergence of sequences of subspaces in an inner product space\",\"authors\":\"Prasanta Malik, Saikat Das\",\"doi\":\"10.56947/gjom.v17i1.2082\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we introduce the notion of ℑ-convergence of sequences of k-dimensional subspaces of an inner product space, where ℑ is an ideal of subsets of ℕ, the set of all natural numbers and k⊂ℕ. We also study some basic properties of this notion.\",\"PeriodicalId\":421614,\"journal\":{\"name\":\"Gulf Journal of Mathematics\",\"volume\":\"51 6\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Gulf Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56947/gjom.v17i1.2082\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gulf Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56947/gjom.v17i1.2082","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文介绍了内积空间 k 维子空间序列的ℑ-收敛概念,其中ℑ是所有自然数的集合ℕ的理想子集,而 k⊂ℕ是所有自然数的集合。我们还将研究这一概念的一些基本性质。
I- Convergence of sequences of subspaces in an inner product space
In this paper we introduce the notion of ℑ-convergence of sequences of k-dimensional subspaces of an inner product space, where ℑ is an ideal of subsets of ℕ, the set of all natural numbers and k⊂ℕ. We also study some basic properties of this notion.