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

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 $\phi$-biflatness and left $\phi$-biprojectivity. We show that left $\phi$-biflatness and left $\phi$-biprojectivity are closely related to the notions of left $\phi$-amenability and $\phi$-inner amenability. We characterize left $\phi$-biprojectivity and left $\phi$-biflatness of certain semigroup algebras and some algebras related to a locally compact group. We discuss non left $\phi$-biflatness of some specified triangular Banach algebras.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 14 April 2024

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