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Invariant subspaces for polynomially bounded operators |
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| Affiliation: | a Mathematical Institute, Romanian Academy, P.O. Box 1-764, RO 70700 Bucharest, Romania b Institute of Mathematics, Czech Academy of Sciences, ?itná 25, 115 67 Prague, Czech Republic |
| Abstract: | Let T be a polynomially bounded operator on a Banach space X whose spectrum contains the unit circle. Then T∗ has a nontrivial invariant subspace. In particular, if X is reflexive, then T itself has a nontrivial invariant subspace. This generalizes the well-known result of Brown, Chevreau, and Pearcy for Hilbert space contractions. |
| Keywords: | primary 47A15 secondary 47A60 |
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