φ-Approximate Biprojective and (φ-Ψ) Amenable Banach Algebras

Abstract

We introduce and study the concept of φ-approximate biprojective and (φ-Ψ)-amenable Banach algebra A, where φ is a continuous homomorphism on A and ---. We show that if A is (φ-Ψ)-amenable then there exists a bounded net (mα) in (A ⊗ˆA) such that || mα · φ(a) − ψ ◦ φ(a) · mα ||→ 0 and ψ ◦ π(mα) · φ(a) → φ(a)  for all a ∈ A.

Key words and phrases. Banach algebra, φ-approximate biprojective, φ-approximate biflat.

2000 Mathematics Subject Classification. 43A20, 46H25