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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Small into-isomorphisms between spaces of continuous functions


Author: Y. Benyamini
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
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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\Vert f \right\Vert \leqslant \left\Vert {Tf} \right\Vert \leqslant (1 + \varepsilon )\left\Vert f \right\Vert$ for all $ f \in C(K)$, then there is an isometry $ W$ of $ C(K)$ into $ C(S)$ with $ \left\Vert {T - W} \right\Vert \leqslant 3\varepsilon $. We also give an example to show that this is no longer true when $ K$ is not assumed to be metrizable.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627674-2
Article copyright: © Copyright 1981 American Mathematical Society