Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T17:41:29.276Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized Lipschitz Algebras

Published online by Cambridge University Press:  20 November 2018

E.R. Bishop
E.R. Bishop*
Affiliation:
University of Waterloo, Waterloo, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

A correction has been issued for this article:

Corrections