Into isomorphisms of spaces of continuous functions
HTML articles powered by AMS MathViewer
- by Krzysztof Jarosz PDF
- Proc. Amer. Math. Soc. 90 (1984), 373-377 Request permission
Abstract:
If $X$ and $Y$ are locally compact Hausdorff spaces and $T$ is a linear map from an extremely regular subspace of ${C_0}\left ( X \right )$ into ${C_0}\left ( Y \right )$ such that $|| T |||| {{T^{ - 1}}} || < 2$, then $X$ is a continuous image of a subset of $Y$.References
- D. Amir, On isomorphisms of continuous function spaces, Israel J. Math. 3 (1965), 205–210. MR 200708, DOI 10.1007/BF03008398
- Y. Benyamini, Small into-isomorphisms between spaces of continuous functions, Proc. Amer. Math. Soc. 83 (1981), no. 3, 479–485. MR 627674, DOI 10.1090/S0002-9939-1981-0627674-2
- 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, A generalization of the Banach-Stone theorem, Proc. Amer. Math. Soc. 40 (1973), 426–430. MR 320723, DOI 10.1090/S0002-9939-1973-0320723-6
- W. Holsztyński, Continuous mappings induced by isometries of spaces of continuous function, Studia Math. 26 (1966), 133–136. MR 193491, DOI 10.4064/sm-26-2-133-136
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 373-377
- MSC: Primary 46E25; Secondary 54C35
- DOI: https://doi.org/10.1090/S0002-9939-1984-0728351-2
- MathSciNet review: 728351