Left $\phi$-biflatness and $\phi$-biprojectivity of certain Banach algebras with applications

Left $ϕ$ -biflatness and $ϕ$ -biprojectivity of certain Banach algebras with applications

Articles in Press

Document Type : Original Article

Authors

¹ Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

² Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran

³ Department of Mathematics Faculty of Basic Science, Ilam University, P.O. Box 69315-516 Ilam, Iran

Abstract

This paper continues the investigation initially begun for left

ϕ

-biflatness and left

ϕ

-biprojectivity. We show that left

ϕ

-biflatness and left

ϕ

-biprojectivity are closely related to the notions of left

ϕ

-amenability and

ϕ

-inner amenability. We characterize left

ϕ

-biprojectivity and left

ϕ

-biflatness of certain semigroup algebras and some algebras related to a locally compact group. We discuss non left

ϕ

-biflatness of some specified triangular Banach algebras.

Keywords

Main Subjects