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

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  01 March 2016

YEMON CHOI
YEMON CHOI*
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK email [email protected]
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Abstract

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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].

Keywords

generalised Lau product

MSC classification

Primary: 46H20: Structure, classification of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 2 , October 2016 , pp. 286 - 289
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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