Canadian Mathematical Bulletin ( IF 0.655 ) Pub Date : 2020-09-07 , DOI: 10.4153/s0008439520000740
Fatemeh Abtahi

Let $\mathcal A$ and $\mathcal B$ be commutative and semisimple Banach algebras and let $\theta \in \Delta (\mathcal B)$ . In this paper, we prove that $\mathcal A\times _{\theta }\mathcal B$ is a type I-BSE algebra if and only if ${\mathcal A}_e$ and $\mathcal B$ are so. As a main application of this result, we prove that $\mathcal A\times _{\theta }\mathcal B$ is isomorphic with a $C^*$ -algebra if and only if ${\mathcal A}_e$ and $\mathcal B$ are isomorphic with $C^*$ -algebras. Moreover, we derive related results for the case where $\mathcal A$ is unital.

down
wechat
bug