ORDER ISOMORPHISMS OF LITTLE LIPSCHITZ ALGEBRAS

For compact metric spaces (X, dX) and (Y, dY) and scalars α, β ∈ (0, 1), we prove that every order isomorphism T between little Lips-chitz algebras lip(X, dαX) and lip(Y, d β Y) is a weighted composition operator of the form T (f) = a · (f ◦ h) for all f ∈ lip(X, dαX), where a is a nonvan-ishing positive function in lip(Y, dβY) and h is a Lipschitz homeomorphism from (Y, dβY) onto (X, d α X)