共查询到20条相似文献,搜索用时 31 毫秒
1.
Benoît Pruvost 《Integral Equations and Operator Theory》2002,44(4):480-493
The analytic equivalence of two operators is a generalization of similarity. We prove that under some conditions the analytic equivalence between two Hilbert space operatorsT andR implies the similarity of their restrictions on generalized ranges. We also prove that, in certain cases, the similarity ofT to a contraction implies that ofR. An improvement of a well-known criterion of similarity to an isometry due to Sz.-Nagy is given and an extension of a result of Apostol is obtained. 相似文献
2.
G. J. Groenewald M. A. Petersen Y. Zucker 《Integral Equations and Operator Theory》1997,28(4):466-491
For an arbitrary rational matrix function, not necessarily analytic at infinity, the existence of a right canonical Wiener-Hopf factorization is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. All formulas are based on a special representation of a rational matrix function involving a quintet of matrices. 相似文献
3.
Boris Freydin 《Integral Equations and Operator Theory》1997,29(2):211-230
Ball in [Ba] showed that the commutant lifting theorem for the nest algebras due to Paulsen and Power gives a unified approach to a wide class of interpolation problems for nest algebras. By restricting our attention to the case when nest algebras associated with the problems are discrete we derive a variant of the commutant lifting theorem which avoids language of representation theory and which is sufficient to treat an analog of the generalized Schur-Nevannlinna-Pick (SNP) problem in the setting of upper triangular operators. 相似文献
4.
Vladimir Ryzhov 《Integral Equations and Operator Theory》2008,60(4):539-571
We construct the symmetric functional model of an arbitrary closed operator with non-empty resolvent set acting on a separable
Hilbert space. The construction is based on the explicit form of the Sz.-Nagy-Foiaş model of a closed dissipative operator,
the Potapov-Ginzburg transform of characteristic functions, and certain resolvent identities. All considerations are carried
out under minimal assumptions, and obtained results are directly applicable to problems typically arising in mathematical
physics. Explicit formulae for all the objects participating in the model construction are provided.
相似文献
5.
We consider upper-triangular 2-by-2 operator matrices and are interested in the set that has to be added to certain spectra of the matrix in order to get the union of the corresponding spectra of the two diagonal operators. We show that in the cases of the Browder essential approximate point spectrum, the upper semi-Fredholm spectrum, or the lower semi-Fredholm spectrum the set in question need not to be an open set but may be just a singleton. In addition, we modify and extend known results on Hilbert space operators to operators on Banach spaces. 相似文献
6.
Gabriel T. Prjitur 《Integral Equations and Operator Theory》2002,44(3):359-369
We study the following problem: given a set of holes in the semi-Fredholm domain of an operator, is there an invariant subspace of the operator such that the spectrum of the restriction is equal to the spectrum of the operator together with the set of holes? 相似文献
7.
We provide an alternate approach to an intertwining lifting theorem obtained by Ball, Trent and Vinnikov. The results are an exact analogue of the classical Sz-Nagy-Foias theorem in the case of multipliers on a class of reproducing kernel spaces, which satisfy the Nevanlinna-Pick property. 相似文献
8.
On closures of joint similarity orbits 总被引:1,自引:0,他引:1
For an n-tuple T=(T1,..., Tn) of operators on a Hilbert spacexxHx, the joint similarity orbit of T isxxSx(T)={VTV–1 =(VT1V–1,...,VTnV–1): V is invertible onxxHx}. We study the structure of the norm closure ofxxSx, both in the case when T is commutative and when it is not. We first develop a Rota-model for the Taylor spectrum and use it to study n-tuples with totally disconnected Taylor spectrum, in particular quasinilpotent ones. We then consider limits of nilpotent n-tuples, and of normal n-tuples. For noncommuting n-tuples, we present a number of surprising facts relating the closure ofxxSx(T) to the Harte spectrum of T and the lack of commutativity of T. We show that a continuous function which is constant onxxSx(T) for all T must be constant. We conclude the paper with a detailed study of closed similarity orbits.Research partially supported by grants from the National Science Foundation. 相似文献
9.
D. V. Yakubovich 《Integral Equations and Operator Theory》1995,23(3):353-371
In [6] (after Clancey's work [2]), Martin and Putinar introduced their two-dimensional functional model of a hyponormal operator, which reduces it to the multiplication by the independent variable in a space of distributions. Here we define another model which does (almost) the same for the adjoint operator. We also explain a close relation between these two models and dual bundle shift models of linear operators introduced in [13]. As application, an estimate of the effectual rational multiplicity of hyponormal operators is given.The research described in this publication was made possible in part by Grant No. NW8000 from the International Science Foundation 相似文献
10.
Dan Timotin 《Integral Equations and Operator Theory》2002,42(4):493-497
A simple coupling argument is seen to provide an alternate proof of the weighted commutant lifting theorem of Biswas, Foias and Frazho (which includes, as a particular case, the abstract Nehari theorem of Treil and Volberg). 相似文献
11.
Animikh Biswas 《Integral Equations and Operator Theory》1997,28(4):373-381
In this note, we prove a harmonic-type maximal principle for the Schur parametrization of all intertwining liftings of an intertwining contraction in the commutant lifting theorem. 相似文献
12.
Schôichi Ôta 《Integral Equations and Operator Theory》2006,54(4):555-569
In this paper, q-deformed circularity of an operator in a Hilbert space is introduced and investigated. In particular, the q-deformed circularity of a weighted shift is characterized by an integer, which is uniquely determined by the operator. It
is shown that that the spectrum of a q-deformed circular weighted shift is the whole complex plane. 相似文献
13.
Bamdad R. Yahaghi 《Linear algebra and its applications》2008,428(4):1151-1168
In this paper we consider collections of compact (resp. Cp class) operators on arbitrary Banach (resp. Hilbert) spaces. For a subring R of reals, it is proved that an R-algebra of compact operators with spectra in R on an arbitrary Banach space is triangularizable if and only if every member of the algebra is triangularizable. It is proved that every triangularizability result on certain collections, e.g., semigroups, of compact operators on a complex Banach (resp. Hilbert) space gives rise to its counterpart on a real Banach (resp. Hilbert) space. We use our main results to present new proofs as well as extensions of certain classical theorems (e.g., those due to Kolchin, McCoy, and others) on arbitrary Banach (resp. Hilbert) spaces. 相似文献
14.
Using Scott Brown's techniques, J. Eschmeier and B. Prunaru showed that if T is the restriction of a decomposable (or S-decomposable) operator B to an invariant subspace such that (T) is dominating in C/S for some closed set S, then T has an invariant subspace. In the present paper we prove various invariant subspace theorems by weakening the decomposability condition on B and strengthening the thickness condition on (T).The research is supported by a grant from the Institute for Studies in Theoretical Physics and Mathematics (IRAN). 相似文献
15.
We investigate frequently hypercyclic and chaotic linear operators from a measure-theoretic point of view. Among other things, we show that any frequently hypercyclic operator T acting on a reflexive Banach space admits an invariant probability measure with full support, which may be required to vanish on the set of all periodic vectors for T ; that there exist frequently hypercyclic operators on the sequence space c0 admitting no ergodic measure with full support; and that if an operator admits an ergodic measure with full support, then it has a comeager set of distributionally irregular vectors. We also give some necessary and sufficient conditions (which are satisfied by all the known chaotic operators) for an operator T to admit an invariant measure supported on the set of its hypercyclic vectors and belonging to the closed convex hull of its periodic measures. Finally, we give a Baire category proof of the fact that any operator with a perfectly spanning set of unimodular eigenvectors admits an ergodic measure with full support. 相似文献
16.
Israel Gohberg Seymour Goldberg Naum Krupnik 《Integral Equations and Operator Theory》2001,40(4):441-453
SupposeA is a bounded linear operator on a separable Hilbert space withA
m
of trace class for some positive integerm. A generalized determinant for the operatorI–A is defined, its properties studied and this determinant is then used to exhibit an inversion formula forI–A. 相似文献
17.
Agler's abstract model theory is applied to the family of hyponormal contractions. A sufficient condition for an operator to be extremal in this family is given, and this is used to show that the boundary, or smallest model, for the family is the whole family. 相似文献
19.
Máté Matolcsi 《Journal of Functional Analysis》2003,205(2):401-413
The aim of this paper is to give a characterization in Hilbert spaces of the generators of C0-semigroups associated with closed, sectorial forms in terms of the convergence of a generalized Trotter's product formula. In the course of the proof of the main result we also present a similarity result which can be of independent interest: for any unbounded generator A of a C0-semigroup etA it is possible to introduce an equivalent scalar product on the space, such that etA becomes non-quasi-contractive with respect to the new scalar product. 相似文献
20.
We prove that every one-dimensional extension of a bitriangular operator has a cyclic commutant. We also prove that ifT is an extension of a bitriangular operator by an algebraic operator, then the weakly closed algebraW(T) generated byT has a separating vector.This work was partially supported by NSF Grant DMS-9401544.Participant, Workshop in Linear Analysis and Probability, Texas A&M University 相似文献