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18th International Conference on Operator Theory
June 27 - July 1, 2000
University of the West
Timisoara, Romania

Organizers
Dumitru Gaspar, Traian Ceausu, Aurelian Craciunescu, Aurelian Gheondea, Radu-Nicolae Gologan, Ciprian Pop, Dan Popovici, Nicolae Suciu, Alexandru Terescenco, Dan Timotin, Flavius Turcu

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Invariant subspaces and spectral localization
by
Bebe Prunaru
Institute of Mathematics of the Romanian Academy

For any bounded operator T on some complex Banach space X, we introduce the notion of localizable spectrum, which in case T has property (\delta) coincides with the usual spectrum. We show that every Hilbert space operator whose localizable spectrum is dominating in an open set has a nontrivial invariant subspace. As a corollary, if T is a hyponormal operator with thick spectrum, then every operator quasisimilar to T has a nontrivial invariant subspace.

Date received: May 31, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeo-40.