Journal of Operator Theory

Volume 73, Issue 1, Summer 2015 pp. 127-142.

Hyperinvariant subspaces for some compact perturbations of multiplication operators

Authors: Hubert Klaja
Author institution: Laboratoire Paul Painlevé, UMR 8524, Université Lille 1, 59655 Villeneuve d'Ascq Cedex, France

Summary: In this paper, a sufficient condition for the existence of hyperinvariant subspace of compact perturbations of multiplication operators on some Banach spaces is presented. An interpretation of this result for compact perturbations of normal and diagonal operators on Hilbert space is also discussed. An improvement of a result of Fang and Xia $($Invariant subspaces for certain finite-rank perturbations of diagonal operators, J. Funct. Anal. $(263)(2012)$, 1356-1377) for compact perturbations of diagonal operators is also obtained.

DOI: http://dx.doi.org/10.7900/jot.2013oct06.2011
Keywords: Invariant subspace problem, hyperinvariant subspace problem, compact perturbations of normal operators, compact perturbations of diagonal operators.

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