Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T21:05:34.217Z Has data issue: false hasContentIssue false
  • English
  • Français

APPROXIMATE ISOMETRIES ON FINITE-DIMENSIONAL NORMED SPACES

Published online by Cambridge University Press:  01 July 1999

S. J. DILWORTH
S. J. DILWORTH
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
Get access

Abstract

Every ε-isometry between real normed spaces of the same finite dimension which maps the origin to the origin may be uniformly approximated to within 2ε by a linear isometry. Under a smoothness hypothesis, necessary and sufficient conditions are obtained for the same conclusion to hold for a given ε-isometry between infinite-dimensional Banach spaces.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 4 , July 1999 , pp. 471 - 476
Copyright
© The London Mathematical Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)