Module approximate biprojectivity and module approximate biflatness of Banach algebras

Suppose that A is a Banach algebra and FA is its enveloping dual Banach algebra, we show that FA is approximately contractible (approximately amenable) if A has the same property. Also, we study the relation between the pseudoamenability of FA and the pseudoamenability of the second dual A∗∗ and we also characterize approximate biflatness and approximate biprojectivity of FA associated with approximate biflatness and approximate biprojectivity of the second dual A∗∗.

Section: Introductionmentioning

confidence: 99%

Enveloping Dual Banach Algebras and Approximate Properties

Razi,

Pourabbas

2024

“…Te module cohomological properties for Banach algebras, namely, module (approximate) biprojectivity and module (approximate) bifatness for Banach algebras which are generalization of the classical cases, were introduced in [6,7]. In these papers, the authors found necessary and sufcient conditions for l 1 (S) to be module approximately biprojective and module approximately bifat, where S is an inverse semigroup.…”

Section: Introductionmentioning

confidence: 99%

Some Characterizations for Approximate Biflatness of Semigroup Algebras

Razi

Sahami

2023

In this paper, we study an approximate biflatness of l 1 S , where S is a Clifford semigroup. Indeed, we show that a Clifford semigroup algebra l 1 S is approximately biflat if and only if every maximal subgroup of S is amenable, E S is locally finite, and l 1 S has an approximate identity in c 00 S . Moreover, we prove that l 1 S is approximately biflat if and only if each maximal subgroup of S is amenable for an inverse semigroup S such that E S , the set of its idempotent elements, is totally ordered and locally finite.

“…Module amenable-like properties of Banach algebras which are the generalizations of the classical case have been introduced and studied in Refs. [5,6].…”

Section: Introductionmentioning

confidence: 99%

Approximate Biprojectivity of ℓ¹‐Munn Banach Algebras

Zarei

Pourabbas

Rostami

et al. 2022

In the present paper, we study the approximate biprojectivity and weak approximate biprojectivity of ℓ 1 -Munn Banach algebras when the related sandwich matrix is regular over Inv A . In fact, we show that a ℓ 1 -Munn Banach algebra with the regular sandwich matrix over Inv A is approximately biprojective (weak approximately biprojective) if and only if A is approximately biprojective (weak approximately biprojective), respectively. We also study approximate biprojectivity of upper triangular Banach algebra when the associated sandwich matrix with elements in Inv A is invertible. Finally, we apply our results to Rees semigroup algebras.