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ISOMETRIES OF THE UNITE SPHERE
马玉梅
数学物理学报(英文版). 1992 (4):
366-373.
It is extended that DARYL TINGLEY's results about that isometries between the unit spheres of finite dimensional Banach Spaces necessarily map antipodal points to antipodal points. Now, the results is obtained in strictly convex (or l1) spaces, i.e.:If X, Y are two strictly convex (or l1) spaces, and S(X), S(Y) are the unit spheres of X and Y respectively,f:S(X)onto→S(Y) is an isometry, then f(-x)=-f(x), for any x in S(X).
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