Weak <i>ω</i> ‐Approximate Biprojectivity of Banach Algebras

For a given Banach algebra and a continuous endomorphism ω on , we define weakly ω ‐approximately biprojective and weakly ω ‐approximately Helemskii biflat Banach algebras. We then examine the relationship between them and express the correlation between them and ω ‐pseudoamenability. In addition, we show that if ω is not an idempotent continuous endomorphism on , then is weak ω ‐approximately biprojective. Here, represents the free group on two generators, and denotes the Fourier algebra of .