Hilbert space structure and positive operators

Details Hilbert space structure and positive operators Hilbert space structure and positive operators

2008-05-30

arxiv.org/abs/0805.4721v1

Journal of Mathematical Analysis and Applications 305 (2) (2005), pp. 560-565

Mathematics

Functional Analysis

Scientific paper

10.1016/j.jmaa.2004.12.007

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.

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