Symmetrically pseudo-amenable Banach algebras

TL;DR

This paper introduces the concept of symmetric pseudo-amenability in Banach algebras, explores its properties, compares it with other amenability types, and investigates related derivations.

Contribution

It defines and analyzes a new form of amenability called symmetric pseudo-amenability, including examples and its relation to existing concepts.

Findings

Characterization of symmetric pseudo-amenable Banach algebras

Comparison with other amenability notions

Applications to Jordan and Lie derivations

Abstract

We introduce and study a new notion of amenability called symmetric pseudo-amenability. We obtain some properties of symmetrically pseudo-amenable Banach algebras and with examples, we compare this type of amenability with some other types of amenability. We also provide some special classes of symmetrically pseudo-amenable Banach algebras. Finally, Jordan and Lie derivations from a class of Banach algebras into appropriate Banach bimodules are investigated using the notion of symmetric pseudo-amenability.