Fourier transforms of bounded bilinear forms on \(C^*(S_{1})\times C^*(S_{2})\) of foundation \(*\)-semigroups \(S_{1}\) and \(S_{2}\)
type: Item
instance of: scholarly article
title: Fourier transforms of bounded bilinear forms on \(C^*(S_{1})\times C^*(S_{2})\) of foundation \(*\)-semigroups \(S_{1}\) and \(S_{2}\)
zbMATH Open document ID: 1149.43006
publication date: 2008-09-09T00:00:00Z
review text: A foundation semigroup is a locally compact topological semigroup which carries a suitable analogue of the group algebra \(L^1(G)\) of a locally compact group. In the paper under review the author introduces the \(C^*\)-algebra \(C^*(S)\) and the \(W^*\)-algebra \(W^*(S)\) of a foundation \(*\)-semigroup \(S\). Using these algebras, the author defines the Fourier transforms of bounded bilinear forms on \(C^*(S_1)\times C^*(S_2)\) of two foundation semigroups \(S_1\) and \(S_2\), and gives a characterization of these Fourier transforms in terms of Jordan \(*\)-representations, hemihomogeneous random fields, and weakly harmonizable random fields of \(S_1\) and \(S_2\) into the Hilbert space.
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 43A10
zbMATH DE Number: 5323393
zbMATH Keywords: topological semigroups
zbMATH Keywords: Banach \(*\)-algebras
zbMATH Keywords: representations
zbMATH Keywords: positive definite functions
zbMATH Keywords: Fourier transforms
zbMATH Keywords: bilinear forms
author: Mahmood Lashkarizadeh Bami
reviewed by: Sergei S. Platonov
MaRDI profile type: Publication
full work available at URL: s10114-007-1023-8
OpenAlex ID: W2119185364
cites work: Algebras of Measures on a Locally Compact Semigroup Iii
cites work: Q3704373
cites work: Representations of Foundation Semigroups and their Algebras
cites work: Banach algebras and the general theory of \(^*\)-algebras. II: \(^*\)-algebras
cites work: Q3701927
cites work: Some results on the Fourier-Stieltjes algebra of a locally compact group
cites work: Positive functionals on Lau Banach \(*\)-algebras with application to negative-definite functions on foundation semigroups
cites work: Q3254057
cites work: The Dual Space of an Operator Algebra
cites work: Characterization of Fourier-Stieltjes transforms of vector and operator valued measures
cites work: Noncommutative Fourier transforms of bounded bilinear forms and completely bounded multilinear operators
DOI: 10.1007/S10114-007-1023-8
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5323393