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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
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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

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