Character Inner Amenability of Certain Banach Algebras

TL;DR

This paper investigates the property of character inner amenability in specific Banach algebras, including tensor products, Lau products, and module extensions, providing theoretical insights and examples.

Contribution

It introduces the concept of character inner amenability for various classes of Banach algebras and explores their properties and examples.

Findings

Character inner amenability is established for certain tensor, Lau, and module extension Banach algebras.

Examples illustrating the concept are provided.

Theoretical conditions for character inner amenability are discussed.

Abstract

Character inner amenability for certain class of Banach algebras consist of projective tensor product $A\hat{\otimes}B$, Lau product $A\times_\theta B$ and module extension $A\oplus X$ are investigated. Some illuminating examples are also included.