关于Hilbert空间上一致代数之间的同态

IF 0.7 3区 数学 Q2 MATHEMATICS
Verónica Dimant, J. Singer
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引用次数: 0

摘要

研究了向量值谱Mu,∞(Bl2,Bl2),它是从Au(Bl2)(Bl2上一致连续全纯函数的代数)到H∞(Bl 2上有界全纯函数代数)的一组非零代数同态。该集合自然地投影到H∞(Bl2,l2)的闭单元球上,从而产生相关的纤维化。将I.J.Schark(1961)引入的聚类集的经典概念扩展到向量值谱,我们定义了向量值聚类集。本文的目的是研究纤维和簇集之间的关系,从而获得关于这些簇集中存在解析球的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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来源期刊
Studia Mathematica
Studia Mathematica 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
72
审稿时长
5 months
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.
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