Triviality of the generalized Lau product associated to a Banach algebra homomorphism

Choi, Yemon (2016) Triviality of the generalized Lau product associated to a Banach algebra homomorphism. Bulletin of the Australian Mathematical Society, 94. pp. 286-289. ISSN 0004-9727

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Abstract

Several papers have, as their raison d'etre, the exploration of the generalized Lau product associated to a homomorphism $T:B\to A$ of Banach algebras. In this short note, we demonstrate that the generalized 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 generalized Lau product, and an older construction of Monfared (Studia Mathematica, 2007).