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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