Robin J. Deeley, Department of Mathematics and Statistics, University of Victoria, PO Box 3060 Stn CSC, Victoria, BC Canada V8W 3R4; email: rjdeeley@uvic.ca

Abstract/Résumé:

To a bounded linear operator and a vector in the Hilbert space on which it acts we associate a linear map which we call the orbit operator. We prove a number of results linking properties of the range of the orbit operator to the existence of invariant subspaces of the original operator.

On associe à un opérateur \(T\) et un vecteur \(x\) dans un espace de Hilbert, un opérateur “d’orbite” \(\mathcal{O}_T^{e_i}(x)\), et on démontre des résultats reliant les propriétés de l’image de \(O^{e_i}_T(x)\) et des sous-espaces invariants de \(T\).

Keywords: contractions, cyclic vectors, invariant subspaces

AMS Subject Classification: Invariant subspaces 47A15

PDF(click to download): The Range of the Orbit Operator and Invariant Subspaces