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

#### Authors

Yemon Choi

MSC 2010: 46H20

DOI: 10.1017/S0004972715001823

#### Status

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

Preprint version available at arXiv 1511.07868

#### Abstract

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).