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Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces.

A. Rodríguez Palacios — 1996

Revista Matemática de la Universidad Complutense de Madrid

For a Banach space X, we show how the existence of a norm-one element u in X and a norm-one continuous bilinear mapping f: X x X --> X satisfying f(x,u) = f(u,x) = x for all x in X, together with some more intrinsic conditions, can be utilized to characterize X as a member of some relevant subclass of the class of Banach spaces.

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