A generalization of the Banach-Stone theorem
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- by Bahattin Cengiz PDF
- Proc. Amer. Math. Soc. 40 (1973), 426-430 Request permission
Abstract:
In this paper the following generalization of the Banach-Stone theorem is proved: If $\phi$ is a linear isomorphism of an extremely regular linear subspace of ${C_0}(X)$ onto such a subspace of ${C_0}(Y)$ with $||\phi ||\;||{\phi ^{ - 1}}|| < 2$ then $X$ and $Y$ are homeomorphic.References
- D. Amir, On isomorphisms of continuous function spaces, Israel J. Math. 3 (1965), 205–210. MR 200708, DOI 10.1007/BF03008398
- Michael Cambern, On isomorphisms with small bound, Proc. Amer. Math. Soc. 18 (1967), 1062–1066. MR 217580, DOI 10.1090/S0002-9939-1967-0217580-2
- Bahattin Cengiz, On extremely regular function spaces, Pacific J. Math. 49 (1973), 335–338. MR 358317
- S. B. Myers, Banach spaces of continuous functions, Ann. of Math. (2) 49 (1948), 132–140. MR 23000, DOI 10.2307/1969119
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 426-430
- MSC: Primary 46E15; Secondary 54C99
- DOI: https://doi.org/10.1090/S0002-9939-1973-0320723-6
- MathSciNet review: 0320723