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Isometries of Noncompact Lipschitz Spaces

Published online by Cambridge University Press:  20 November 2018

Nik Weaver
Nik Weaver*
Affiliation:
Mathematics Department, University of California, Santa Barbara, California 93106 U.S.A.
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Abstract

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We show that under reasonable restrictions on the metric spaces X and Y, every surjective isometric isomorphism between Lip(X) and Lip(Y) arises in a simple manner from an isometry between X and Y. Our result differs from several previous results along these lines in that we do not require X and Y to be compact.

Keywords

46B0446E1554E35

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 242 - 249
Copyright
Copyright © Canadian Mathematical Society 1995

References

[C] Conway, J. B., A Course in Functional Analysis, Graduate Texts in Math. 96, Springer-Verlag, 1985.Google Scholar
[dL] de Leeuw, K., Banach spaces of Lipschitz functions, Studia Math. 21(1961/62), 55—66.Google Scholar
[JP] Jarosz, K. and Pathak, V. D., Isometries between function spaces, Trans. Amer. Math. Soc. 305(1988), 193–206.Google Scholar
[Je] Jenkins, T. M., Banach Spaces of Lipschitz Functions on an Abstract Metric Space, Ph.Q thesis, Yale University, 1968.Google Scholar
[Jo] Johnson, J. A., Banach spaces of Lipschitz functions and vector-valued Lipschitz functions, Trans. Amer. Math. Soc. 148(1970), 147–169.Google Scholar
[MW] Mayer-Wolf, E., Isometries between Banach spaces of Lipschitz functions, Israel J. Math. 38(1981), 58–74.Google Scholar
[R] Roy, A. K., Extreme points and linear isometries of the Banach space of Lipschitz functions, Canad. J. Math. 20(1968), 1150–1164.Google Scholar
[V] Vasavada, M. H., Closed Ideals and Linear Isometries of Certain Function Spaces, Ph.D thesis, University of Wisconsin, 1969.Google Scholar
[W] Weaver, N., Lattices of Lipschitz functions, Pacific J. Math. 164(1994), 179–193.Google Scholar