On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras. (6th July 2022) - Sahami, Amir; Shariati, Seyedeh Fatemeh
Abstract : In this paper, we investigate the existence of an ultra central approximate identity for a Banach algebra A and its second dual A ∗ ∗ . Also, we prove that for a left cancellative regular semigroup S, ℓ 1 S ∗ ∗ has an ultra central approximate identity if and only if S is a group. As an application, we show that for a left cancellative semigroup S, ℓ 1 S ∗ ∗ is pseudo-contractible if and only if S is a finite group. We also study this property for φ -Lau product Banach algebras and the module extension Banach algebras.