Left \phi-biprojectivity of some classes of abstract Segal algebras

In this paper, we investigate left \phi-biprojectivity of Segal algebras and abstract Segal algebras. We show that for some abstract Segal algebras with some mild conditions left \phi-biprojectivity is equivalent with left \phi-contractibility. Also, we characterize left \phi-biprojectivity of a Segal algebra S(G) in the terms of compactness of G, where G is a locally compact group. We introduce a class of abstract Segal algebras among Triangular Banach algebras. We show that  some abstract Segal algebras related to triangular Banach algebras are not biprojective.

Keywords:

Left phi-biprojective , Triangular Banach algebra , Left phi-contractible , Segal algebra , Locally compact group