A bound-two isomorphism between $C(X)$ Banach spaces
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- by H. B. Cohen PDF
- Proc. Amer. Math. Soc. 50 (1975), 215-217 Request permission
Abstract:
Nonhomeomorphic compact Hausdorff spaces $X$ and $Y$ and an isomorphism $\phi :C(X) \to C(Y)$ (onto) are constructed such that $||\phi ||\;||{\phi ^{ - 1}}|| = 2$. Amir had asked if such a $\phi$ exists with $||\phi ||\;||{\phi ^{ - 1}}|| < 3$.References
- D. Amir, On isomorphisms of continuous function spaces, Israel J. Math. 3 (1965), 205β210. MR 200708, DOI 10.1007/BF03008398
- Michael Cambern, On isomorphisms with small bound, Proc. Amer. Math. Soc. 18 (1967), 1062β1066. MR 217580, DOI 10.1090/S0002-9939-1967-0217580-2
- Michael Cambern, Isomorphisms of $C_{0}(Y)$ onto $C(X)$, Pacific J. Math. 35 (1970), 307β312. MR 433201
- Y. Gordon, On the distance coefficient between isomorphic function spaces, Israel J. Math. 8 (1970), 391β397. MR 270128, DOI 10.1007/BF02798685
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. MR 0415253
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 215-217
- MSC: Primary 46E15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0380379-5
- MathSciNet review: 0380379