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Invariant subspaces of certain subnormal operators

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
17
Issue
3
Identifiers
DOI: 10.1016/0022-1236(74)90040-8

Abstract

Abstract Let T be a subnormal, nonnormal operator on a Hilbert space and suppose that the point spectrum of T ∗ is empty. Then there exist vectors x ≠ 0 for which (T ∗ − zI) −1x exists and is weakly continuous for all z. It is shown that under certain conditions, the Cauchy integral of this vector function taken around an appropriate contour, not necessarily lying in the resolvent set of T ∗ , leads to a proper (nontrivial) invariant subspace of T ∗ .

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