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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)
##### Keywords:
$$T$$-Lau product; cyclic amenability
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