2019/05/14 by Sahami, Amir
#43A20 #46H05 Secondary 43A07 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46M10
paper · doi:10.48550/arxiv.1905.05552
In this paper, we study left ϕ-biflatness and left ϕ-biprojectivity of some Banach algebras, where ϕ is a non-zero multiplicative linear function. We show that if the Banach algebra A** is left ϕ-biprojective, then A is left ϕ-biflat. Using this tool we study left ϕ-biflatness of some matrix algebras. We also study left ϕ-biflatness and left ϕ-biprojectivity of the projective tensor product of some Banach algebras. We prove that for a locally compact group G, M(G)⊗p A(G) is left ϕ⊗ ψ-biprojective if and only if G is finite. We show that M(G)⊗p L1(G) is left ϕ⊗ ψ-biprojective if and only if G is compact.