A Lattice-valued Banach-Stone Theorem

Jiling Cao, Ivan Reilly and Hongyun Xiong

Abstract

Let $X$ and $Y$ be two compact Hausdorff spaces, and $E$ be a Banach
lattice. We show that if there is a non-vanishing preserving Riesz
isomorphism $Phi: C(X, E) to C(Y)$, then $X$ is homeomorphic to $Y$
and $E$ is Riesz isomorphic to $mathbb R$.

Keywords
Banach lattice, Riesz homomorphism, support, Banach-Stone theorem.

Math Review Classification
Primary 46E05 ; Secondary 46B42, 54C35

Last Updated
March 2000

Length
9 pages

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