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Generalized Lipschitz Algebras

Published online by Cambridge University Press:  20 November 2018

E.R. Bishop
E.R. Bishop*
Affiliation:
University of Waterloo, Waterloo, Ontario
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The purpose of this paper is to generalize the results of Sherbert on Lipschitz algebras and to study the relationship between homomorphisms of these algebras and continuous maps of the underlying metric spaces. In Sections 1, 2, and 3 we associate with each metric space a class of Lipschitz-type algebras and extend Sherbert's results in [7] to this class; in particular Sherbert's theorem 5.1 is extended to non-compact metric spaces (3.3, 3.4, 3.5).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 1 , February 1969 , pp. 1 - 19
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Bourbaki, N., Fonctions d'une Variable Reele (Hermann, 1950).Google Scholar
2. Glaeser, G., Etudes de quelques Algebres Tayloriennes. J. Anal. Math. 6 (1958) 1–124.Google Scholar
3. Nakai, M., On a ring isomorphism induced by quasi-conformal mappings. Nagoya Math. J. 14 (1959) 201–221.Google Scholar
4. Mirkil, H., Continuous translation of Hölder and Lipschitz functions, Canad. J. Math. 12 (1960) 674–685.Google Scholar
5. Kunzi, H.P., Quasikonforme Abbildungen. (Springer-Verlag, 1960).Google Scholar
6. skii, Krasnosel' and Rutickii, , Convex functions and Orlicz spaces. (P. Noordhoff Ltd., 1961).Google Scholar
7. Sherbert, D.R., Banach algebras of Lipschitz functions. Pac. J. Math. 13 (1963) 1387–1399.Google Scholar

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