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

Abstract

For i=1,2, let Ei be a reflexive Banach lattice over R with a certain parameter lambda+(Ei)>1, let Ki be a locally compact (Hausdorff) topological space and let Hi be a closed subspace of C0(Ki,Ei) such that each point of the Choquet boundary ChHiKi of Hi is a weak peak point. We show that if there exists an isomorphism T:H1 -> H2 with T.T-1 < min{lambda+(E1),lambda+(E2)} such that T and T-1 preserve positivity, then ChH1K1 is homeomorphic to ChH2K2.

Keywords

• Function space
• Vector-valued Banach-Stone theorem
• Amir-Cambern theorem
• Banach lattice
• 47B38
• 46A55