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Connes amenability-like properties

Amin Mahmoodi — 2014

Studia Mathematica

We introduce and study the notions of w*-approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We prove that the dual Banach sequence algebra ℓ¹ is not w*-approximately Connes amenable. We show that in general the concepts of pseudo-Connes amenability and Connes amenability are distinct. Moreover the relations between these new notions are also discussed.

Some module cohomological properties of Banach algebras

Elham Ilka; Amin Mahmoodi; Abasalt Bodaghi — 2020

Mathematica Bohemica

We find some relations between module biprojectivity and module biflatness of Banach algebras $𝒜$ and $ℬ$ and their projective tensor product $𝒜 \hat{\otimes} ℬ$ . For some semigroups $S$ , we study module biprojectivity and module biflatness of semigroup algebras $l^{1} (S)$ .

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