A further property of spherical isometries

R. Tanaka


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 \(Y\)




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

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Bulletin of the Aust. Math. Soc., copyright Australian Mathematical Publishing Association Inc.