Vanishing of the first $(\sigma ,\tau )$-cohomology group of triangular Banach algebras

Abstract

In this paper, we define the first topological $(\sigma ,\tau )$-cohomology group and examine vanishing of the first $(\sigma ,\tau )$-cohomology groups of certain triangular Banach algebras. We apply our results to study the $(\sigma ,\tau )$-weak amenability and $(\sigma ,\tau )$-amenability of triangular Banach algebras.

15 pages, Added materials

References in corpus (2)

• Approximately Vanishing of Topological Cohomology Groups
• Hochschild cohomology of triangular matrix algebras