Character pseudo-amenability of Banach algebras (Q2855856)

The authors study the notion of character pseudo-amenability which they define as follows: a Banach algebra \(A\) is character pseudo-amenable if \(A\) has a right approximate identity and a \(\phi\)-approximate diagonal (as defined in [\textit{Z. Hu} et al., Stud. Math. 193, No. 1, 53--78 (2009; Zbl 1175.22005)]) for every character \(\phi\) of \(A\). In particular, the authors give characterisations of character pseudo-amenability of some Banach algebras associated to locally compact groups (many of these algebras are character pseudo-amenable precisely when they are amenable, although the authors show that, in general, character pseudo-amenability is a strictly weaker notion than both character amenability and pseudo-amenability).