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Mathematics > Functional Analysis

arXiv:1903.00051 (math)
[Submitted on 28 Feb 2019 (v1), last revised 7 Mar 2019 (this version, v2)]

Title:On Shilov boundary and Gelfand spectrum of algebras of generalized analytic functions

Authors:A.R. Mirotin
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Abstract:Let $S$ be a discrete abelian semigroup with unit and concellations and $\widehat {S}$ the semigroup of semicharacters of $S$. We shaw that the strong boundary and the Shilov boundary of the algebra of generalized analytic functions defined on $\widehat {S}$ are unions of some maximal subgroups of $\widehat {S}$. We shaw also that the both boundaries coincide with the character group of $S$ if $S$ does not contain nontrivial simple ideals. In the last case the Gelfand spectrum of the algebra under consideration is calculated.
Comments: in Russian
Subjects: Functional Analysis (math.FA)
MSC classes: 43A,
Cite as: arXiv:1903.00051 [math.FA]
  (or arXiv:1903.00051v2 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.1903.00051

Submission history

From: Adolf R Mirotin [view email]
[v1] Thu, 28 Feb 2019 20:09:19 UTC (13 KB)
[v2] Thu, 7 Mar 2019 06:51:50 UTC (13 KB)
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