Some Dense Linear Subspaces of Extended Little Lipschitz Algebras

Abstract EN

Let (X,d) be a compact metric space.

In 1987, Bade, Curtis, and Dales obtained a sufficient condition for density of a subspace P of little Lipschitz algebra lip(X,α) in this algebra and in particular showed that Lip(X,1) is dense in lip(X,α), whenever 0<α<1.

Let K be a compact subset of X.

We define new classes of Lipchitz algebras Lip(X,K,α) for α∈(0,1] and lip(X,K,α) for α∈(0,1), consisting of those continuous complex-valued functions f on X such that f|K∈Lip(K,α) and f|K∈lip(K,α), respectively.

In this paper we obtain a sufficient condition for density of a linear subspace P of extended little Lipschitz algebra lip(X,K,α) in this algebra and in particular show that Lip(X,K,1) is dense in lip(X,K,α), whenever 0<α<1.