Abstract
An example is given proving that there exist two separable Banach spaces which are uniformly homeomorphic but not isomorphic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Aharoni and J. Lindenstrauss,Uniform equivalence between Banach spaces, Bull. Am. Math. Soc.84 (1978), 281–283.
M. M. Day,Convolutions, means, and spectra, Ill. J. Math.8 (1964), 100–111.
P. Enflo,Uniform homeomorphisms between Banach spaces, Seminaire Maurey-Schwartz 1975–1976, Exposé 18.
S. Heinrich and P. Mankiewicz,Application of ultraproducts to the uniform and Lipschitz classification of Banach spaces, Studia Math.73 (1982), 225–251.
P. Mankiewicz,On Lipschitz mappings between Fréchet spaces, Studia Math.41 (1972), 225–241.
S. Mazur,Une remarque sur l'homéomorphie des champs fonctionnels, Studia Math.1 (1930), 83–85.
M. Ribe,On uniformly homeomorphic normed spaces, Ark. Mat.14 (1976), 237–244.
M. Ribe,On uniformly homeomorphic normed spaces II, Ark. Mat.16 (1978), 1–9.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ribe, M. Existence of separable uniformly homeomorphic nonisomorphic Banach spaces. Israel J. Math. 48, 139–147 (1984). https://doi.org/10.1007/BF02761159
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02761159