关于Hilbert空间上一致代数之间的同态

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2021-02-12 DOI:10.4064/sm210219-10-6

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。

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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 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

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.