On the Lipschitz Operator Algebras

In a recent paper by H. X. Cao, J. H. Zhang and Z. B. Xu an α-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 α-Lipschitz operator if and only if for each σ ∈ X∗ the mapping σ ◦ F is a α-Lipschitz function. The Lipschitz operators algebras Lα(K,A) and lα(K,A) are developed here further, and we study their amenability and weak amenability of these algebras. Moreover, we prove an interesting result that Lα(K,A) and lα(K,A) are isometrically isomorphic to Lα(K)⊗̌A and lα(K)⊗̌A respectively. Also we study homomorphisms on the LA(X,B).