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), The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.4721 or http://arXiv.org/abs/0805.4721 or by email in unzipped form by transmitting an empty message with subject line uget 0805.4721 or in gzipped form by using subject line get 0805.4721 to: math@arXiv.org.