希尔伯特模的一类亲C^* -代数和有界元

IF 0.7 Q2 MATHEMATICS

Tbilisi Mathematical Journal Pub Date : 2021-06-01 DOI:10.32513/tmj/19322008122

Morteza Kardel, R. Sanati

{"title":"希尔伯特模的一类亲C^* -代数和有界元","authors":"Morteza Kardel, R. Sanati","doi":"10.32513/tmj/19322008122","DOIUrl":null,"url":null,"abstract":"In this paper, introducing the notion of topologically simple pro $C^*$-algebras, we show that direct product of $C^*$-algebras $K(H_i)$, as the set of all compact operators on a Hilbert space $H_i$, is a topologically simple pro $C^*$-algebra. Applying this fact, we prove that the set of all bounded elements of a certain class of Hilbert modules are dense in the same module.","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A certain class of pro $C^*$-algebras and bounded elements of a Hilbert module\",\"authors\":\"Morteza Kardel, R. Sanati\",\"doi\":\"10.32513/tmj/19322008122\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, introducing the notion of topologically simple pro $C^*$-algebras, we show that direct product of $C^*$-algebras $K(H_i)$, as the set of all compact operators on a Hilbert space $H_i$, is a topologically simple pro $C^*$-algebra. Applying this fact, we prove that the set of all bounded elements of a certain class of Hilbert modules are dense in the same module.\",\"PeriodicalId\":43977,\"journal\":{\"name\":\"Tbilisi Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tbilisi Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32513/tmj/19322008122\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tbilisi Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32513/tmj/19322008122","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文引入拓扑简单pro$C^*$-代数的概念，证明了作为Hilbert空间$H_i$上所有紧算子的集合的$C^*$代数$K（H_i）$的直积是一个拓扑简单pro-C^*$代数。应用这个事实，我们证明了一类Hilbert模的所有有界元素的集合在同一个模中是稠密的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A certain class of pro $C^*$-algebras and bounded elements of a Hilbert module

In this paper, introducing the notion of topologically simple pro $C^*$-algebras, we show that direct product of $C^*$-algebras $K(H_i)$, as the set of all compact operators on a Hilbert space $H_i$, is a topologically simple pro $C^*$-algebra. Applying this fact, we prove that the set of all bounded elements of a certain class of Hilbert modules are dense in the same module.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Tbilisi Mathematical Journal MATHEMATICS-

自引率

0.00%

发文量