TRIVIALITY OF THE GENERALISED LAU PRODUCT ASSOCIATED TO A BANACH ALGEBRA HOMOMORPHISM

TRIVIALITY OF THE GENERALISED LAU PRODUCT ASSOCIATED TO A BANACH ALGEBRA HOMOMORPHISM

Several papers have, as their raison d’être, the exploration of the generalised Lau product associated to a homomorphism $T:B\rightarrow A$ of Banach algebras. In this short note, we demonstrate that the generalised Lau product is isomorphic as a Banach algebra to the usual direct product $A\oplus B...

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2016-10, Vol.94 (2), p.286-289
1. Verfasser: CHOI, YEMON
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Banach spaces
Homomorphisms
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description Several papers have, as their raison d’être, the exploration of the generalised Lau product associated to a homomorphism $T:B\rightarrow A$ of Banach algebras. In this short note, we demonstrate that the generalised Lau product is isomorphic as a Banach algebra to the usual direct product $A\oplus B$ . We also correct some misleading claims made about the relationship between this generalised Lau product and an older construction of Monfared [‘On certain products of Banach algebras with applications to harmonic analysis’, Studia Math. 178(3) (2007), 277–294].
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subjects Banach spaces
Homomorphisms
title TRIVIALITY OF THE GENERALISED LAU PRODUCT ASSOCIATED TO A BANACH ALGEBRA HOMOMORPHISM
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