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Isometries of the unit sphere   总被引:35,自引:0,他引:35  
It is shown that isometries between the unit spheres of finite dimensional Banach spaces necessarily map antipodal points to antipodal points.  相似文献
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D. P. Mil'man and V. D. Mil'man considered sequences of decreasing nonempty closed bounded convex sets with empty intersection to obtain characteristics of non-reflexivity. They showed that in every nonreflexive space there is such a sequence which is ω-separated. We show that in every nonreflexive space there is also always such a sequence which is not ω-separated  相似文献
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