Small into-isomorphisms between spaces of continuous functions
HTML articles powered by AMS MathViewer
- by Y. Benyamini PDF
- Proc. Amer. Math. Soc. 83 (1981), 479-485 Request permission
Abstract:
We prove that if $K$ is a compact metric space, $0 < \varepsilon < 1$, and $T$ is an operator from $C(K)$ into $C(S)$ satisfying $\left \| f \right \| \leqslant \left \| {Tf} \right \| \leqslant (1 + \varepsilon )\left \| f \right \|$ for all $f \in C(K)$, then there is an isometry $W$ of $C(K)$ into $C(S)$ with $\left \| {T - W} \right \| \leqslant 3\varepsilon$. We also give an example to show that this is no longer true when $K$ is not assumed to be metrizable.References
- D. Amir, On isomorphisms of continuous function spaces, Israel J. Math. 3 (1965), 205โ210. MR 200708, DOI 10.1007/BF03008398
- Y. Benyamini, Near isometries in the class of $L^{1}$-preduals, Israel J. Math. 20 (1975), no.ย 3-4, 275โ281. MR 377571, DOI 10.1007/BF02760332
- Michael Cambern, On isomorphisms with small bound, Proc. Amer. Math. Soc. 18 (1967), 1062โ1066. MR 217580, DOI 10.1090/S0002-9939-1967-0217580-2
- Michael Cambern, On $L^{1}$ isomorphisms, Proc. Amer. Math. Soc. 78 (1980), no.ย 2, 227โ228. MR 550500, DOI 10.1090/S0002-9939-1980-0550500-6
- H. H. Corson and J. Lindenstrauss, On simultaneous extension of continuous functions, Bull. Amer. Math. Soc. 71 (1965), 542โ545. MR 174951, DOI 10.1090/S0002-9904-1965-11321-0
- 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 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 479-485
- MSC: Primary 46E15; Secondary 46B25
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627674-2
- MathSciNet review: 627674