The hyperinvariant subspace problem for quasi-$n$-hyponormal operators
Commun. Korean Math. Soc. 2007 Vol. 22, No. 3, 383-389 Printed September 1, 2007
An-Hyun Kim, Eun-Young Kwon Changwon National University, Changwon National University
Abstract : In this paper we examine the hyperinvariant subspace problem for quasi-$n$-hyponormal operators. The main result on this problem is as follows. If $T=N+K$ is such that $N$ is a quasi-$n$-hyponormal operator whose spectrum contains an exposed arc and $K$ belongs to the Schatten $p$-ideal then $T$ has a non-trivial hyperinvariant subspace.
Keywords : $n$-normal operators, quasi-$n$-hyponormal operators, hyperinvariant subspace problem
