Journal of Operator Theory

Volume 36, Issue 1, Summer 1996 pp. 147-156.

Hyperinvariant subspaces for certain compact perturbations of an operator

Authors: Isabelle Chalendar
Author institution:U.F.R. Mathématiques et Informatique, Université Bordeaux I, 351, Cours de la Libération, 33405 Talence Cedex, FRANCE

Summary: Let A, B be linear operators acting in a Hilbert space, such that B or AB is in a von Neumann-Schatten class $\mathcal C_p$. Sufficient conditions on the geometry of the spectrum and on the growth of the resolvent are given for the existence of hyperinvariant subspaces of A + B.

Keywords: Operator, Hilbert space, hyperinvariant subspace, Growth of the resolvent, compact perturbation and Neumann-Schatten class.

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