More on cyclic amenability of the Lau product of Banach algebras defined by a Banach algebra morphism

Abstract

For two Banach algebras $A$ and $B$, the $T$-Lau product $A{\times }_{T}B$, was recently introduced and studied for some bounded homomorphism $T:B\to A$ with $\Vert T\Vert \le 1$. Here, we give general nessesary and sufficent conditions for $A{\times }_{T}B$ to be (approximately) cyclic amenable. In particular, we extend some recent results on (approximate) cyclic amenability of direct product $A\oplus B$ and $T$-Lau product $A{\times }_{T}B$ and answer a question on cyclic amenability of $A{\times }_{T}B$.

arXiv commentTo appear in Math. Slovaca