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

Publication at Faculty of Mathematics and Physics |
2021

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.