Some Hilbert Space Characterizations and Banach Space Inequalities
Tae-Hwa Kim, Hong‐Kun Xu · Mathematical Inequalities & Applications · 1998
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.