A multiplicative convolution on the spectra of algebras of symmetric analytic functions
type: Item
instance of: scholarly article
title: A multiplicative convolution on the spectra of algebras of symmetric analytic functions
zbMATH Open document ID: 1321.46054
author: Irina Chernega
author: Pablo Galindo
author: A. V. Zagorodnyuk
published in: Revista Matemática Complutense
publication date: 2014-09-25T00:00:00Z
review text: Let \(H_{bs}(l_p)\) denote the algebra of all symmetric analytic functions on \(l_p\) that are bounded on bounded sets endowed with the topology of the uniform convergence on the bounded sets and by \(M_{bs}(l_p)\) the spectrum of \(H_{bs}(l_p)\), that is, the set of all non-zero continuous complex-valued homomorphisms. In [J. Math. Anal. Appl. 395, No.~2, 569--577 (2012; Zbl 1258.46021)], the authors defined a symmetric convolution operation in \(M_{bs}(l_p)\) which made it possible to obtain a representation of \(M_{bs}(l_1)\) in terms of entire functions of exponential type. It was then unknown to the authors whether this representation is onto. In the paper under review, they introduce a multiplicative convolution operation in \(M_{bs}(l_1)\) that allows them to show that such a representation is not onto.
reviewed by: Mikael Lindström
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 46G25
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 46G20
zbMATH DE Number: 6347549
zbMATH Keywords: polynomials and analytic functions on Banach spaces
zbMATH Keywords: symmetric polynomials
zbMATH Keywords: spectra of algebras
MaRDI profile type: Publication
full work available at URL: s13163-013-0128-0
OpenAlex ID: W2020843247
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cites work: ON POLYNOMIAL APPROXIMATION OF FUNCTIONS ON HILBERT SPACE
DOI: 10.1007/S13163-013-0128-0
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description: scientific article; zbMATH DE number 6347549