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More on cyclic amenability of the Lau product of Banach algebras defined by a Banach algebra morphism. (English) Zbl 06842068
Summary: 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 \(\|T\|\le 1\). Here, we give general nessesary and sufficent conditions for \(A\times_TB\) 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 \(A\times_TB\) and answer a question on cyclic amenability of \(A\times_TB\).
MSC:
46H05 General theory of topological algebras
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
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