|
|||||
|
|
Hilbert space structure and positive operators |
|
| Authors: | Dimosthenis Drivaliaris |
| Institution: | a Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Str., 82100 Chios, Greece b Department of Mathematics, School of Applied Mathematics and Natural Sciences, National Technical University of Athens, Iroon Polytexneiou 9, 15780 Zografou, Greece |
| 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 nonsymmetric case. |
| Keywords: | Positive operator Symmetric operator Hilbert space characterization Equivalent norm Complemented subspace Accretive operator |
| 本文献已被 ScienceDirect 等数据库收录！ | |