A lattice-valued Banach-Stone theorem

Author： Cao J.   Reilly I.   Xiong H.  

Publisher： Springer Publishing Company

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.98, Iss.1-2, 2003-01, pp. : 103-110

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Abstract

Let X and Y be compact Hausdorff spaces, and let E be a Banach lattice. In this short note, we show that if there exists a Riesz isomorphismΦ:C(X, E) →C(Y, R) such that Φ(f) has no zeros if f has none, then X is homeomorphic to Y and E is Riesz isomorphic to R.

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