Approximate amenability of tensor products of Banach algebras (Q2360024)

The authors investigate the relationship between the approximate amenability of two Banach algebras \(A\) and \(B\) and their projective tensor product \(A\hat\otimes B\). They present several conditions under which the approximate amenability of \(A\hat\otimes B\) implies the approximate amenability of \(A\) and \(B\). They also give an example of two boundedly approximately amenable Banach algebras such that their tensor product is not approximately amenable.