APPROXIMATE BIPROJECTIVITY AND φ-BIFLATNESS OF CERTAIN BANACH ALGEBRAS

In the first part of the paper, we investigate the approximate biprojectivity of some Banach algebras related to the locally compact groups. We show that a Segal algebra S(G) is approximate biprojective if and only if G is compact. Also for every continuous weight w, we show that L-1 (G, w) is approximate biprojective if and only if G is compact, provided that w(g) >= 1 for every g is an element of G. In the second part, we study phi-biflatness of some Banach algebras, where 0 is a character. We show that if S(G) is phi(0)-biflat, then G is an amenable group, where phi(0) is the augmentation character on S(G). Finally, we show that the phi-biflatness of L-1(G)** implies the amenability of G.