A FURTHER PROPERTY OF SPHERICAL ISOMETRIES

作者：Tanaka Ryotaro^*

来源：Bulletin of the Australian Mathematical Society, 2014, 90(2): 304-310.

DOI：10.1017/S0004972714000185

• Tingley%26apos
• s problem
• isometric extension problem
• frame
• k-extreme point

In this paper, it is proved that every isometry between the unit spheres of two real Banach spaces preserves the frames 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.

• 出版日期2014-10