IDEALS, POINT DERIVATIONS, AMENABILITY an‎d WEAK AMENABILITY OF EXTENDED LIPSCHITZ ALGEBRAS

Let (X; d) be a compact metric space and let K be a nonempty compact subset of X: Let 2 (0; 1] and let Lip(X;K; d denote the algebra of all f 2 C(X) for which fjK 2 Lip(K; d). In this paper we rst study the structure of certain ideals of the algebra Lip(X;K; d). Next we show that if K is innite and int(K) contains a limit point of K then Lip(X;K; d) has at least a nonzero continuous point derivation and applying this fact we prove that Lip(X;K; d) is not weakly amenable and amenable