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.
Eskandari, R., & Mirzapour, F. (2015). Hyperinvariant subspaces and quasinilpotent operators. Bulletin of the Iranian Mathematical Society, 41(4), 805-813.
MLA
R. Eskandari; F. Mirzapour. "Hyperinvariant subspaces and quasinilpotent operators". Bulletin of the Iranian Mathematical Society, 41, 4, 2015, 805-813.
HARVARD
Eskandari, R., Mirzapour, F. (2015). 'Hyperinvariant subspaces and quasinilpotent operators', Bulletin of the Iranian Mathematical Society, 41(4), pp. 805-813.
VANCOUVER
Eskandari, R., Mirzapour, F. Hyperinvariant subspaces and quasinilpotent operators. Bulletin of the Iranian Mathematical Society, 2015; 41(4): 805-813.
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