Hyperinvariant subspaces for quasinilpotent operators on Hilbert spaces
نویسندگان
چکیده
منابع مشابه
Hyperinvariant subspaces and quasinilpotent operators
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.
متن کاملhyperinvariant subspaces and quasinilpotent operators
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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In this article we employ a technique originated by Enflo in 1998 and later modified by the authors to study the hyperinvariant subspace problem for subnormal operators. We show that every “normalized” subnormal operator S such that either {(S∗nSn)1/n} does not converge in the SOT to the identity operator or {(SnS∗n)1/n} does not converge in the SOT to zero has a nontrivial hyperinvariant subsp...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2008.09.063