Banach-stone theorem for Banach lattice valued continuous functions

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Ercan Z., Onal S.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.135, no.9, pp.2827-2829, 2007 (SCI-Expanded) identifier identifier


Let Chi and Upsilon be compact Hausdor spaces, Epsilon be a Banach lattice and F be an AM space with unit. Let pi : C(X, E) -> C(Upsilon, F) be a Riesz isomorphism such that 0 not subset of f (X) if and only if 0 not subset of pi (f)(Upsilon) for each f is an element of C(Chi, Epsilon). We prove that Chi is homeomorphic to Upsilon and Epsilon is Riesz isomorphic to F. This generalizes some known results.