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Banach-Stone theorems and Riesz algebras. (English) Zbl 1102.46017
Let \(X, Y\) be compact Hausdorff spaces and let \(E, F\) be both Banach lattices and Riesz algebras. In this paper, the following main result shall be proved: If \(F\) has no zero-divisor and there exists a Riesz algebraic isomorphism \(\Phi:C(X,E)\to C(Y,F)\) such that \(\Phi(f)\) has no zero if \(f\) has none, then \(X\) is homeomorphic to \(Y\) and \(E\) is Riesz algebraically isomorphic to \(F\).

46B42 Banach lattices
46H05 General theory of topological algebras
Full Text: DOI
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