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An Elementary Approach to a Lattice-Valued Banach-Stone Theorem
並列摘要
Let X and Y be compact Hausdorff spaces, and E be a nonzero real Banach lattice. In this note, we give an elementary proof of a lattice-valued Banach-Stone theorem by Cao, Reilly and Xiong [3] which asserts that if there exists a Riesz isomorphism Ф: C(X,E)→C(Y,R) such that Ф(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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