Abstract. In the rst 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 L1(G;w) is approximate biprojective if and only if G is compact, provided that w(g) 1 for every g 2 G. In the second part, we study -bi atness of some Banach algebras, where is a character. We show that if S(G) is 0-bi at, then G is an amenable group, where 0 is the augmentation character on S(G). Finally, we show that the -bi atness of L1(G) implies the amenability of G.
