# Hyperinvariant subspaces and quasinilpotent operators

Document Type : Research Paper

Authors

Department of‎ ‎Mathematics‎, ‎University‎ ‎of Zanjan‎, ‎P.O‎. ‎Box 45195-313‎, ‎Zanjan‎, ‎Iran

Abstract

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

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### History

• Receive Date: 08 February 2014
• Revise Date: 07 May 2014
• Accept Date: 07 May 2014