{"title":"关于Hilbert空间上一致代数之间的同态","authors":"Verónica Dimant, J. Singer","doi":"10.4064/sm210219-10-6","DOIUrl":null,"url":null,"abstract":"We study the vector-valued spectrum Mu,∞(Bl2 , Bl2 ) which is the set of nonzero algebra homomorphisms from Au(Bl2 ) (the algebra of uniformly continuous holomorphic functions on Bl2) to H∞(Bl2 ) (the algebra of bounded holomorphic functions on Bl2 ). This set is naturally projected onto the closed unit ball of H∞(Bl2 , l2) giving rise to an associated fibering. Extending the classical notion of cluster sets introduced by I. J. Schark (1961) to the vector-valued spectrum we define vector-valued cluster sets. The aim of the article is to look at the relationship between fibers and cluster sets obtaining results regarding the existence of analytic balls into these sets.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A look into homomorphisms between uniform algebras\\nover a Hilbert space\",\"authors\":\"Verónica Dimant, J. Singer\",\"doi\":\"10.4064/sm210219-10-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the vector-valued spectrum Mu,∞(Bl2 , Bl2 ) which is the set of nonzero algebra homomorphisms from Au(Bl2 ) (the algebra of uniformly continuous holomorphic functions on Bl2) to H∞(Bl2 ) (the algebra of bounded holomorphic functions on Bl2 ). This set is naturally projected onto the closed unit ball of H∞(Bl2 , l2) giving rise to an associated fibering. Extending the classical notion of cluster sets introduced by I. J. Schark (1961) to the vector-valued spectrum we define vector-valued cluster sets. The aim of the article is to look at the relationship between fibers and cluster sets obtaining results regarding the existence of analytic balls into these sets.\",\"PeriodicalId\":51179,\"journal\":{\"name\":\"Studia Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-02-12\",\"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/sm210219-10-6\",\"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/sm210219-10-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A look into homomorphisms between uniform algebras
over a Hilbert space
We study the vector-valued spectrum Mu,∞(Bl2 , Bl2 ) which is the set of nonzero algebra homomorphisms from Au(Bl2 ) (the algebra of uniformly continuous holomorphic functions on Bl2) to H∞(Bl2 ) (the algebra of bounded holomorphic functions on Bl2 ). This set is naturally projected onto the closed unit ball of H∞(Bl2 , l2) giving rise to an associated fibering. Extending the classical notion of cluster sets introduced by I. J. Schark (1961) to the vector-valued spectrum we define vector-valued cluster sets. The aim of the article is to look at the relationship between fibers and cluster sets obtaining results regarding the existence of analytic balls into these sets.
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.