vix.ing · top · new · best · stats · spec

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

2019/02/28 by Mirotin, A. R.
#43A #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1903.00051

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.

Related