Generalized biprojectivity and biflatness of abstract Segal algebras

Abstract

We investigate generalized amenability, contractibility, biprojectivity and biflatness properties of various classes of abstract Segal algebras with respect to the Banach algebra A. Moreover, we verify some of the previous available results about Segal algebras, for abstract Segal algebras.

Biprojectivity and Biflatness of Lau Product of Banach Algebras Defined by a Banach Algebra Morphism

“…We refer to [5] as a standard reference in this field. Moreover, we refer to recent work, such as [1,4,9,12,14], closely related to the present work. The main purpose of this paper is to study biprojectivity and biflatness of A × ϕ B.…”

Harmonic functionals on certain Banach algebras

“…We denote by ∆(A) the set of all non-zero characters, bounded multiplicative linear functionals on A. For φ ∈ ∆(A), Kaniuth, Lau and Pym [11,12] introduced and investigated a notion of amenability for Banach algebras called φ-amenability; see also [1,2,9,19]. In fact, A is said to be φ-amenable if there exists m ∈ A * * such that m(φ) = 1 and m(f • a) = φ(a) m(f ) for all f ∈ A * and a ∈ A, where f • a ∈ A * is defined by (f • a)(b) = f (ab) for all b ∈ A.…”