An Amir-Cambern theorem for subspaces of Banach lattice-valued continuous functions

Abstract

For i = 1, 2, let E i be a reflexive Banach lattice over R with a certain parameter λ + (E i ) > 1, let K i be a locally compact (Hausdorff) topological space and let H i be a closed subspace of C 0 (K i , E i ) such that each point of the Choquet boundary Ch H i K i of H i is a weak peak point. We show that if there exists an isomorphism T :2010 Mathematics Subject Classification. 47B38; 46A55.