Hyperinvariant subspaces and quasinilpotent operators

Document Type : Research Paper


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


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.


Main Subjects