A new class of ideal Connes amenability

TL;DR

This paper introduces a new concept called $\sigma$-Connes ideal amenability for dual Banach algebras, extending existing notions and exploring their properties and implications.

Contribution

It defines the $\sigma$-Connes ideal amenability, shows its equivalence to ideal Connes amenability under certain conditions, and provides general results and examples.

Findings

$\sigma$-Connes ideal amenability is introduced as a new notion.

Under certain conditions, $\sigma$-Connes ideal amenability coincides with ideal Connes amenability.

The paper presents properties, hereditary results, and examples of this new amenability concept.

Abstract

In this paper, we introduce a new notion of amenability, $\sigma-$Connes ideal, say, for a large class of dual Banach algebras. We extend the concept of ideal Connes amenability and study their properties. Let $\sigma$ be a $weak^{*}$-continuous endomorphism on a dual Banach algebra $\mathcal{A}$ with dense range. Then the concept of ideal Connes-amenability and $\sigma-$ ideally Connes amenability are the same. We gave some general results and hereditary properties with some examples for this new notion of amenability.