Banach-Stone theorem for Banach lattice valued continuous functions
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- by Z. Ercan and S. Önal PDF
- Proc. Amer. Math. Soc. 135 (2007), 2827-2829 Request permission
Abstract:
Let $X$ and $Y$ be compact Hausdorff spaces, $E$ be a Banach lattice and $F$ be an AM space with unit. Let ${\pi }:C(X,E)\rightarrow C(Y,F)$ be a Riesz isomorphism such that $0\not \in f(X)$ if and only if $0\not \in {\pi }(f)(Y)$ for each $f\in C(X,E)$. We prove that $X$ is homeomorphic to $Y$ and $E$ is Riesz isomorphic to $F$. This generalizes some known results.References
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Additional Information
- Z. Ercan
- Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
- Email: zercan@metu.edu.tr
- S. Önal
- Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
- Email: osul@metu.edu.tr
- Received by editor(s): June 16, 2005
- Received by editor(s) in revised form: May 21, 2006
- Published electronically: May 8, 2007
- Communicated by: Joseph A. Ball
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 2827-2829
- MSC (2000): Primary 46E40; Secondary 46B42
- DOI: https://doi.org/10.1090/S0002-9939-07-08788-6
- MathSciNet review: 2317958