[Banach] Abstract of a paper by D. Drivaliaris and N. Yannakakis

This is an announcement for the paper "Hilbert space structure and positive operators" by D. Drivaliaris and N. Yannakakis.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46B03; 46C15; 47B99

Citation: Journal of Mathematical Analysis and Applications 305 (2) (2005),

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