%0 Journal Article
%T Hilbert space structure and positive operators
%A D. Drivaliaris
%A N. Yannakakis
%J Mathematics
%D 2008
%I arXiv
%R 10.1016/j.jmaa.2004.12.007
%X Let X be a real Banach space. We prove that the existence of an injective, positive, symmetric and not strictly singular operator from X into its dual implies that either X admits an equivalent Hilbertian norm or it contains a nontrivially complemented subspace which is isomorphic to a Hilbert space. We also treat the non-symmetric case.
%U http://arxiv.org/abs/0805.4721v1