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 کاملFrames of subspaces and operators
We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H. We get sufficient conditions on an orthonormal basis of subspaces E = {Ei}i∈I of a Hilbert space K and a surjective T ∈ L(K,H) in order that {T (Ei)}i∈I is a frame of subspaces with respect to a computable sequence of weights. We also o...
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.
متن کاملOperators with Common Hypercyclic Subspaces
We provide a reasonable sufficient condition for a family of operators to have a common hypercyclic subspace. We also extend a result of the third author and A. Montes [22], thereby obtaining a common hypercyclic subspace for certain countable families of compact perturbations of operators of norm no larger than one.
متن کاملLocal Operators in Krylov Subspaces
For a bounded linear operator A on a Hilbert space H we study local spectral sets and their relation to the spectrum of the local operator. By the local operator we mean A restricted to a Krylov subspace spanfb; Ab; A 2 b; :::g for a generic b 2 H. Moreover we investigate the relation between (A), the spectrum of A, and the spectrum of the local operator. Also spectral properties of the spectru...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2010
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2010.01.001