arXiv subjects

R. J. Loy

Publications and source records attributed to R. J. Loy.

2 recordsLinked to original sources

arXiv2019

Approximate semi-amenability of Banach algebras

In recent work of the authors the notion of a derivation being approximately semi-inner arose as a tool for investigating (approximate) amenability questions for Banach algebras. Here we investigate this property in its own right, together with the consequent one of approximately semi-amenability. Under certain hypotheses regarding approximate identities this new notion is the same as approximate amenability, but more generally it covers some important classes of algebras which are not approximately amenable, in particular Segal algebras on amenable SIN-groups.

math.FA↗

arXiv2016

Approximate amenability of tensor products of Banach algebras

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.

math.FA↗