A further property of spherical isometries

Authors

  • R. Tanaka Niigata University

Keywords:

Tingley's problem, isometric extension problem, frame, k-extreme point

Abstract

In this paper, it is proved that every isometry between the unit spheres of two real Banach spaces preserves the frame of the unit balls. As a consequence, if \(X\) and \(Y\) are \(n\)-dimensional Banach spaces and \(T_0\) is an isometry from the unit sphere of \(X\) onto that of \(Y\) then it maps the set of all \((n-1)\)-extreme points of the unit ball of \(X\) onto that of \(Y\) DOI: 10.1017/S0004972714000185

Author Biography

R. Tanaka, Niigata University

Department of Mathematical Science, Graduate School of Science and Technology

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles
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