Hyperinvariant subspaces and quasinilpotent operators
نویسندگان
چکیده مقاله:
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.
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 for Some Subnormal Operators
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...
متن کاملHyperinvariant Subspaces for Some B–circular Operators
We show that if A is a Hilbert–space operator, then the set of all projections onto hyperinvariant subspaces of A, which is contained in the von Neumann algebra vN(A) that is generated by A, is independent of the representation of vN(A), thought of as an abstract W∗–algebra. We modify a technique of Foias, Ko, Jung and Pearcy to get a method for finding nontrivial hyperinvariant subspaces of ce...
متن کاملHyperinvariant Subspaces for Some Operators on Locally Convex Spaces
Some results concerning hyperinvariant subspaces of some operators on locally convex spaces are considered. Denseness of a class of operators which have a hyperinvariant subspace in the algebra of locally bounded operators is proved.
متن کاملMODULUS HYPERINVARIANT CLOSED IDEALS FOR QUASINILPOTENT OPERATORS WITH MODULUS ON lp-SPACES
In this paper, it is proved that every non-zero continuous operator with modulus on an lp-space whose modulus is quasinilpotent at a non-zero positive vector has a non-trivial modulus hyperinvariant closed ideal. AMS Subject Classification: 47A15
متن کاملHyperinvariant subspaces and extended eigenvalues
An extended eigenvalue for an operator A is a scalar λ for which the operator equation AX = λXA has a nonzero solution. Several scenarios are investigated where the existence of non-unimodular extended eigenvalues leads to invariant or hyperinvariant subspaces. For a bounded operator A on a complex Hilbert space H, the set EE(A) of extended eigenvalues for A is defined to be the set of those co...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 41 شماره 4
صفحات 805- 813
تاریخ انتشار 2015-08-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023