Abstract
It is well known that if X is a normed linear space with dimension not less than three such that the radial projection from X onto the closed unit ball is nonexpansive, then X must be an inner product space. Using this fact, we are able to give a characterization of Hilbert spaces. Two other Hilbert space characterizations and some Banach space inequalities are established via duality maps. Mathematics subject classification (1991): Primary 46B20; Secondary 47H09.
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