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

Abstract

Several papers have, as their raison d'etre, the exploration of the \emph{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).

5 pages, CC-BY licence. v2: some minor corrections. Final version, incorporating referee's comments. To appear in Bull. Austral. Math. Soc. v3: only change is to remove an accidental duplicate entry in the bibliography

References in corpus (3)

• Some homological properties of T-Lau product algebra
• Cohomological characterization of $T$-Lau product algebras
• The multiplier algebra and BSE-functions for certain product of Banach algebras