C. R. Math. Rep. Acad. Sci. Canada Vol. 29 (4) 2007, pp. 123–127
December 30, 2007
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 \(T\).
AMS Subject Classification: Invariant subspaces 47A15
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