A new class of ideal Connes amenability

Year 2024, Early Access, 1 - 12

Ahmad Minapoor , Ali Rejali , Mohammad Javad Mehdıpour

https://doi.org/10.15672/hujms.1372448

Abstract

In this paper, we introduce the notion of σ−ideally Connes amenable for dual Banach algebras and give some hereditary properties for this new notion. We also investigate σ−ideally Connes amenability of ℓ1(G,ω). We show that if ω is a diagonally bounded weight function on discrete group G and σ is isometrically isomorphism of ℓ1(G,ω), then ℓ1(G,ω) is σ−ideally Connes amenable and so it is ideally Connes amenable.

Keywords

Dual Banach algebra, Amenability, Ideal Connes amenable, Group algebra

References

• [1] U. Bader, T. Gelander and N. Monod, A fixed point theorem for L 1 spaces, Invent. Math. 189 (1), 143-148, 2012.