A further property of spherical isometries

R. Tanaka

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

Keywords


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



Remember, for most actions you have to record/upload into OJS
and then inform the editor/author via clicking on an email icon or Completion button.
Bulletin of the Aust. Math. Soc., copyright Australian Mathematical Publishing Association Inc.