hyperinvariant subspaces and quasinilpotent operators
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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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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 41
issue 4 2015
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