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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 $$F$$.

##### MSC:
 46B42 Banach lattices 46H05 General theory of topological algebras
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##### References:
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