2019/05/14 by Amir Sahami, Sahami, Amir
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Banach Space Theory
paper · pdf · doi:10.48550/arxiv.1905.05556
In this paper, we introduce a homological notion of left ϕ-biprojectivity for Banach algebras, where ϕ is a non-zero multiplicative linear functional. We show that for a locally compact group G, the Segal algebra S(G) is left ϕ-contractible if and only if G is compact. Also, we prove that the Fourier algebra A(G) is left ϕ-biprojective if and only if G is discrete. Finally, we study left ϕ-biprojectivity of certain semigroup algebras. We give some examples which show the differences between our new notion and the classical ones.