Boundaries for Gelfand transform images of Banach algebras of holomorphic functions

2021/10/14 by Yun Sung Choi, Mingu Jung, Choi, Yun Sung +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2110.07196

openalex publication_date 2021/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a Banach algebra of bounded holomorphic functions on the open unit ball B_X of a complex Banach space X. Considering the Gelfand transform image \widehatA of the Banach algebra A, which is a uniform algebra on the spectrum of A, we obtain an explicit description of the Shilov boundary for \widehatA for classical Banach spaces X in the case where A is a certain Banach algebra, for instance, A_∞ (B_X), A_u (B_X) or A_wu (B_X). Some possible application of our result to the famous Corona theorem is also briefly discussed.

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