Nonvanishing Preservers and Compact Weighted Composition Operators between Spaces of Lipschitz Functions

الملخص EN

We will give the α-Lipschitz version of the Banach-Stone type theorems for lattice-valued α-Lipschitz functions on some metric spaces.

In particular, when X and Y are bounded metric spaces, if T:LipX→LipY is a nonvanishing preserver, then T is a weighted composition operator Tf=h·f∘φ, where φ:Y→X is a Lipschitz homeomorphism.

We also characterize the compact weighted composition operators between spaces of Lipschitz functions.