Journal of Operator Theory
Volume 73, Issue 1, Winter 2015 pp. 127-142.
Hyperinvariant subspaces for some compact perturbations of multiplication operators
Authors:
Hubert Klaja
Author institution:Laboratoire Paul Painleve, UMR 8524, Universite 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,
\textit{J. Funct. Anal.}
\textbf{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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