On the analytic α-Lipschitz vector-valued operators

Let (X, d) be a non-empty compact metric space in C, (B, ∥ . ∥) be a commutative unital Banach algebra over the scalar field F(= R or C) and α ∈ R with 0 < α ≤ 1. In this work, first we define the analytic α-Lipschitz B-valued operators on X and denote the Banach algebra of all these operators by Lipα A(X, B). When B = F, we write Lipα A(X) instead of Lipα A(X, B). Then we study some interesting results about Lipα A(X, B), including the relationship between Lipα A(X, B) with Lipα A(X) and B, and also characterize the characters on Lipα A(X, B).