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Extreme Points and Linear Isometries of the Banach Space of Lipschitz Functions

Published online by Cambridge University Press:  20 November 2018

Ashoke K. Roy
Ashoke K. Roy*
Affiliation:
Boston University, Boston, Massachusetts ; Tata Institute of Fundamental Research, Bombay, India
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Let X be a compact metric space with metric d. A complex-valued function ƒ on X is said to satisfy a Lipschitz condition if, for all points x and y of X, there exists a constant K such that

The smallest constant for which the above inequality holds is called the Lipschitz constant for ƒ and is denoted by ||ƒ||d, that is,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1150 - 1164
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

The research in this paper forms part of the author's doctoral dissertation submitted to the Massachusetts Institute of Technology in June, 1966. The author would like to thank Professor K. Hoffman for guidance and encouragement in the course of this research. Thanks are due to the referee for pointing out some errors and for suggesting improvements of presentation in several places.

References

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