Invariant subspaces for bounded operators with large localizable spectrum

Author:
Bebe Prunaru

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2365-2372

MSC (2000):
Primary 47A15, 47B20; Secondary 47A11, 47L45

DOI:
https://doi.org/10.1090/S0002-9939-01-05971-8

Published electronically:
January 17, 2001

MathSciNet review:
1823920

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Suppose is a complex Hilbert space and is a bounded operator. For each closed set let denote the corresponding spectral manifold. Let denote the set of all points with the property that for any open neighborhood of In this paper we show that if is dominating in some bounded open set, then has a nontrivial invariant subspace. As a corollary, every Hilbert space operator which is a quasiaffine transform of a subdecomposable operator with large spectrum has a nontrivial invariant subspace.

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Additional Information

**Bebe Prunaru**

Affiliation:
Institute of Mathematics, Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania

Email:
bprunaru@imar.ro

DOI:
https://doi.org/10.1090/S0002-9939-01-05971-8

Keywords:
Invariant subspaces,
local spectral theory

Received by editor(s):
December 14, 1999

Published electronically:
January 17, 2001

Additional Notes:
The author was partially supported by Grant 5232/1999 from ANSTI

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2001
American Mathematical Society