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On the distance coefficient between isomorphic function spaces

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Abstract

IfX, Y are compact countable metric spaces such thatY contains no subset homeomorphic toX, then for any isomorphismΦ ofC(X) intoC(Y), ‖ φ ‖ ‖ φ−1 ‖≧3. This result and some variants of it are established here, and prove a special case of a conjecture raised in [1].

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Authors and Affiliations

  1. The Hebrew University of Jerusalem, Israel

    Y. Gordon

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  1. Y. Gordon
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Additional information

This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof. J. Lindenstrauss. I wish to thank Prof. Lindenstrauss and Prof. A. Dvoretzky for their guidance and the interest they showed in this work.

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Gordon, Y. On the distance coefficient between isomorphic function spaces. Israel J. Math. 8, 391–397 (1970). https://doi.org/10.1007/BF02798685

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  • DOI: https://doi.org/10.1007/BF02798685

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