Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On a Lipschitz invariant of normed spaces

Author: Yoav Benyamini
Journal: Proc. Amer. Math. Soc. 110 (1990), 979-981
MSC: Primary 46B20
MathSciNet review: 1028040
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: C. Bessaga introduced an invariant $ \eta (X)$ for $ \sigma $-compact normed linear spaces. He showed that $ \eta (X) = \eta (Y)$ whenever $ X$ and $ Y$ are Lipschitz homeomorphic. In this note we construct two $ \sigma $-compact normed spaces with $ \eta (X) = \eta (Y)$ which are not Lipschitz homeomorphic. Moreover, there are no compact convex sets $ K$ and $ L$ generating $ X$ and $ Y$, respectively, which are Lipschitz homeomorphic. This answers two problems posed by Bessaga.

References [Enhancements On Off] (What's this?)

  • [Ben] Y. Benyamini, The uniform classification of Banach spaces, Longhorn Notes, 1984-1985, pp. 15-38. MR 832247
  • [Bes] C. Bessaga, A Lipschitz invariant of normed linear spaces related to the entropy numbers, Rocky Mountain J. Math. 10 (1980), 81-84. MR 573863 (81f:46020)
  • [LT] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Lecture Notes in Math., vol. 338, Springer-Verlag, New York, 1973. MR 0415253 (54:3344)
  • [M] P. Mankiewicz, On the differentiability of Lipschitz mappings in Frechet spaces, Studia Math. 45 (1973), 15-29. MR 0331055 (48:9390)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20

Retrieve articles in all journals with MSC: 46B20

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society