Super pseudo-amenability of Banach algebras and applications to semigroup algebras

This paper introduces the concept of super pseudo-amenable Banach algebras, which extends the established notion of pseudo-amenability. The study focuses on the super pseudo-amenability of Banach algebras associated with locally compact groups, particularly group algebras. Specifically, it is demonstrated that [Formula: see text] is super pseudo-amenable if and only if [Formula: see text] is an amenable [Formula: see text]-group. Additionally, the super pseudo-amenability of certain inverse semigroup algebras is characterized. As an application, it is shown that for the Brandt semigroup [Formula: see text] over a nonempty set [Formula: see text], the algebra [Formula: see text] is super pseudo-amenable if and only if [Formula: see text] is amenable and [Formula: see text] is finite.