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A characterization of isometries on an open convex set

A characterization of isometries on an open convex set Let X be a real Hilbert space with dim X ≥ 2 and let Y be a real normed space which is strictly convex. In this paper, we generalize a theorem of Benz by proving that if a mapping f, from an open convex subset of X into Y, has a contractive distance ρ and an extensive one Nρ (where N ≥ 2 is a fixed integer), then f is an isometry. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

A characterization of isometries on an open convex set

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Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-006-0015-0
Publisher site
See Article on Publisher Site

Abstract

Let X be a real Hilbert space with dim X ≥ 2 and let Y be a real normed space which is strictly convex. In this paper, we generalize a theorem of Benz by proving that if a mapping f, from an open convex subset of X into Y, has a contractive distance ρ and an extensive one Nρ (where N ≥ 2 is a fixed integer), then f is an isometry.

Journal

Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals

Published: Jan 1, 2006

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