This analysis reveals super pseudo-amenability in Banach algebras related to locally compact groups, indicating implications for inverse 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 non-empty 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.
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Rostami et al. (2025) studied this question.
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