The Banach-Stone theorem revisited

Date

2008-10-01

Author

ERCAN, ZAFER
Önal, Süleyman

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Let X and Y be compact Hausclorff spaces, and E and F be locally solid Riesz spaces. If pi : C(X. E) -> C(Y, F) is a 1-biseparating Riesz isomorphism then X and Y are homeomorphic, and E and F are Riesz isomorphic. This generalizes the main results of [Z. Ercan, S. Onal, Banach-Stone theorem for Banach lattice valued continuous functions, Proc. Amer. Math. Soc. 135 (9) (2007) 2827-2829] and [X. Miao, C. Xinhe, H. Jiling, Banach-Stone theorems and Riesz algebras, J. Math. Anal. Appl. 313 (1) (2006) 177-183], and answers a conjecture in [Z. Ercan, S. Onal, Banach-Stone theorem for Banach lattice valued continuous functions. Proc. Amer. Math. Soc. 135 (9) (2007) 2827-2829].

Subject Keywords

Geometry and Topology

URI

https://hdl.handle.net/11511/46879

Journal

TOPOLOGY AND ITS APPLICATIONS

DOI

https://doi.org/10.1016/j.topol.2008.05.018

Collections

Department of Mathematics, Article

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Citation Formats

Z. ERCAN and S. Önal, “The Banach-Stone theorem revisited,” TOPOLOGY AND ITS APPLICATIONS, pp. 1800–1803, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46879.