AMENABILITY AND WEAK AMENABILITY OF LIPSCHITZ OPERATORS ALGEBRAS

In a recent paper by H.X. Cao, J.H. Zhang and Z.B. Xu a -Lipschitz operator from a compact metric space into a Banach space A is defined and characterized in a natural way in the sence that F : K ! A is a -Lipschitz operator if and only if for each 2 X the mapping oF is a -Lipschitz function. The Lipschitz operators algebras L (K,A) and l (K,A) are developed here further, and we study their amenability and weak amenabil- ity of these algebras. Moreover, we prove an interesting result that L (K,A) and l (K,A) are isometrically isomorphic to L (K)ˇ A and l (K)ˇ A respec- tively.