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arXiv · 1604.08681

Approximate amenability of tensor products of Banach algebras

F. Ghahramani·R. J. Loy
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Abstract

We show that the tensor product of approximately amenable algebras need not be approximately amenable, and investigate conditions under which $A$ and $B$ being approximately amenable implies, or is implied by, $A\hat{\otimes}B$ or $A^{\#}\hat{\otimes} B^{\#}$ being approximately amenable. Our methods also enable us to prove that if $A\hat{\otimes}B$ is amenable, then so are $A$ and $B$, a result proved by Barry Johnson in 1996 under an additional assumption.

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BibTeXRIS

F. Ghahramani, R. J. Loy. 2016-04-29. Approximate amenability of tensor products of Banach algebras. https://arxiv.org/abs/1604.08681

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