Hilbert space structure and positive operators
Functional Analysis
2008-06-02 v1
Abstract
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.
Cite
@article{arxiv.0805.4721,
title = {Hilbert space structure and positive operators},
author = {D. Drivaliaris and N. Yannakakis},
journal= {arXiv preprint arXiv:0805.4721},
year = {2008}
}