Operators with a compact imaginary part
Ciprian FoiasSami HamidConstantin OnicaCarl Pearcy
47A15invariant subspacescompact imaginary part
In this note we initiate a study of the old unsolved problem whether every $T \in \mathcal{L}(\mathcal{H})$ of the form $T = H + iK$ with $K$ compact has a nontrivial invariant subspace, using [C. Foias, C. Pasnicu, and D. Voiculescu, \emph{Weak limits of almost invariant projections}, J. Operator Theory \textbf{2} (1979), 79--93] as our main tool. In case $K \geq 0$ we obtain some positive results.
Indiana University Mathematics Journal
2009
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10.1512/iumj.2009.58.3963
10.1512/iumj.2009.58.3963
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Indiana Univ. Math. J. 58 (2009) 2297 - 2304
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