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


Yemon Choi


MSC 2010: 46H20

DOI: 10.1017/S0004972715001823


Appeared as Bull. Austral. Math. Soc. 94 (2016), no. 2, 286–289.

Preprint version available at arXiv 1511.07868


[ Math Reviews | Zentralblatt ]


Several papers have, as their raison d'être, 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).


The backstory to this paper is fleshed out a little in a 2015 MathReview that I wrote: [MR 3294267]

Yemon Choi