{"title":"论拓扑结构的格尔范德理论","authors":"Ali Oukhouya","doi":"10.1007/s41980-023-00854-9","DOIUrl":null,"url":null,"abstract":"<p>We present conditions under which the Gel’fand transform <span>\\(E^{\\wedge },\\)</span> of locally <i>m</i>-convex algebra <i>E</i>, is a dense subalgebra of <span>\\( \\mathcal {C}_{c}(\\mathfrak M(E))\\)</span>. The partition of unity and the local theorem are given for a commutative unital locally <i>m</i>-convex algebra.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Gel’fand Theory for Topological Algebras\",\"authors\":\"Ali Oukhouya\",\"doi\":\"10.1007/s41980-023-00854-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We present conditions under which the Gel’fand transform <span>\\\\(E^{\\\\wedge },\\\\)</span> of locally <i>m</i>-convex algebra <i>E</i>, is a dense subalgebra of <span>\\\\( \\\\mathcal {C}_{c}(\\\\mathfrak M(E))\\\\)</span>. The partition of unity and the local theorem are given for a commutative unital locally <i>m</i>-convex algebra.</p>\",\"PeriodicalId\":9395,\"journal\":{\"name\":\"Bulletin of The Iranian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-03-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Iranian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s41980-023-00854-9\",\"RegionNum\":4,\"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":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-023-00854-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们提出了一些条件，在这些条件下，局部 m 凸代数 E 的 Gel'fand 变换 （E^{\wedge },\）是 \( \mathcal {C}_{c}(\mathfrak M(E))\) 的密集子代数。给出了换元单整局部 m-凸代数的统一分割和局部定理。
We present conditions under which the Gel’fand transform \(E^{\wedge },\) of locally m-convex algebra E, is a dense subalgebra of \( \mathcal {C}_{c}(\mathfrak M(E))\). The partition of unity and the local theorem are given for a commutative unital locally m-convex algebra.
期刊介绍：
The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
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