共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
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
4.
Weyl's theorem for operator matrices 总被引:11,自引:0,他引:11
Woo Young Lee 《Integral Equations and Operator Theory》1998,32(3):319-331
Weyl's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. By comparison Browder's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with Riesz points. Weyl's theorem and Browder's theorem are liable to fail for 2×2 operator matrices. In this paper we explore how Weyl's theorem and Browder's theorem survive for 2×2 operator matrices on the Hilbert space.Supported in part by BSRI-97-1420 and KOSEF 94-0701-02-01-3. 相似文献
5.
In this paper a new lifting interpolation problem is introduced and an explicit solution is given. The result includes the commutant lifting theorem as well as its generalizations in [27] and [2]. The main theorem yields explicit solutions to new natural variants of most of the metric constrained interpolation problems treated in [9]. It is also shown that via an infinite dimensional enlargement of the underlying geometric structure a solution of the new lifting problem can be obtained from the commutant lifting theorem. However, the new setup presented obtained from the commutant lifting theorem. However, the new setup presented in this paper appears to be better suited to deal with interpolations problems from systems and control theory than the commutant lifting theorem.Dedicated to Israel Gohberg, as a token of admiration for his inspiring work in analysis and operator theory, with its far reaching applications, in friendship and with great affection. 相似文献
6.
Weyl's theorem and quasi-similarity 总被引:1,自引:0,他引:1
In Ho Jeon 《Integral Equations and Operator Theory》2001,39(2):214-221
In this paper we give necessary and sufficient conditions of a finitely ascensive operator to obey Weyl's theorem and study Weyl's theorem for quasi-affine transforms. In particular, we give an improvement of the earlier result of Duggal forp-hyponormal operators. 相似文献
7.
Mourad Oudghiri 《Integral Equations and Operator Theory》2005,53(4):535-545
In the present paper we examine the stability of Weyl’s theorem under perturbations. We show that if T is an isoloid operator on a Banach space, that satisfies Weyl’s theorem, and F is a bounded operator that commutes with T and for which there exists a positive integer n such that Fn is finite rank, then T + F obeys Weyl’s theorem. Further, we establish that if T is finite-isoloid, then Weyl’s theorem is transmitted from T to T + R, for every Riesz operator R commuting with T. Also, we consider an important class of operators that satisfy Weyl’s theorem, and we give a more general perturbation results
for this class. 相似文献
8.
Topological uniform descent and Weyl type theorem 总被引:1,自引:0,他引:1
Xiaohong Cao 《Linear algebra and its applications》2007,420(1):175-182
The generalized Weyl’s theorem holds for a Banach space operator T if and only if T or T∗ has the single valued extension property in the complement of the Weyl spectrum (or B-Weyl spectrum) and T has topological uniform descent at all λ which are isolated eigenvalues of T. Also, we show that the generalized Weyl’s theorem holds for analytically paranormal operators. 相似文献
9.
We introduce the class of operators on Banach spaces having property (H) and study Weyl’s theorems, and related results for operators which satisfy this property. We show that a- Weyl’s theorem holds for every decomposable operator having property (H). We also show that a-Weyl’s theorem holds for every multiplier T of a commutative semi-simple regular Tauberian Banach algebra. In particular every convolution operator Tμ of a group algebra L1(G), G a locally compact abelian group, satisfies a-Weyl’s theorem. Similar results are given for multipliers of other important commutative Banach algebras. 相似文献
10.
B.P. Duggal 《Linear algebra and its applications》2006,414(1):271-277
A Banach space operator T is polaroid and satisfies Weyl’s theorem if and only if T is Kato type at points λ ∈ iso σ(T) and has SVEP at points λ not in the Weyl spectrum of T. For such operators T, f(T) satisfies Weyl’s theorem for every non-constant function f analytic on a neighborhood of σ(T) if and only if f(T∗) satisfies Weyl’s theorem. 相似文献
11.
M. G. Krein 《Integral Equations and Operator Theory》1998,30(2):140-162
Some principles of the operator theory in a linear space with two norms are established in this paper. The well-known Hilbert-Schmidt theorem on the eigenfunction expansion of sourcewise represented functions, Mercer's theorem and other results can be consider as special cases of the statements presented. The general approach proposed is used to construct the theory of symmetrizable operators and to investigate the asymptotic behaviour of eigenvalues of compact operators.This paper was translated by M. Gorbuchuk and V. GorbachukThis paper was translated by M. Gorbuchuk and V. Gorbachuk. 相似文献
12.
Yu Kurokawa 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1562-1822
In this paper, we first obtain a weak mean convergence theorem of Baillon’s type for nonspreading mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem for nonspreading mappings in a Hilbert space. 相似文献
13.
This paper studies Weyl's theorems, and some related results for operators with Dunford's property (C). Weyl's theorem in some classes of operators (e.g.M-hyponormal,p-hyponormal and totally paranormal operators) is considered. 相似文献
14.
On a class of quasi-Fredholm operators 总被引:1,自引:0,他引:1
M. Berkani 《Integral Equations and Operator Theory》1999,34(2):244-249
We study a class of bounded linear operators acting on a Banach spaceX called B-Fredholm operators. Among other things we characterize a B-Fredholm operator as the direct sum of a nilpotent operator and a Fredholm operator and we prove a spectral mapping theorem for B-Fredholm operators.IMemory of my father, Sidi-Bouhouria 1914-0991. 相似文献
15.
Animikh Biswas 《Integral Equations and Operator Theory》2000,36(4):396-408
In this note, we prove a harmonic-type maximal principle for the Schur parametrization of all contractive interpolants in the three chains completion problem (see [4]), which is analogous to the maximal principle proven in [2] in case of the Schur parametrization of all contractive intertwining liftings in the commutant lifting theorem. 相似文献
16.
In this paper, we first prove the strict quasi-concavity of maximizing functions, and next, using a generalization of the KKM theorem, we prove two maximum theorems without assuming the upper semicontinuity. As an application, using a common fixed point theorem, the existence theorem of social equilibrium is obtained. Finally, we shall give two illustrative examples of systems of constrained optimization problems. 相似文献
17.
Foias C. Frazho A. E. Gohberg I. Kaashoek M. A. 《Integral Equations and Operator Theory》1997,28(2):158-190
This paper contains a generalization of the commutant lifting theorem to a time-variant setting. The main result, which is called the three chains completion theorem, is used to solve various nonstationary norm constrained interpolation problems. 相似文献
18.
Joseph A. Ball 《Integral Equations and Operator Theory》1996,25(4):377-405
We show how the commutant lifting theorem for nest algebras due to Paulsen and Power can be used to give a unified framework for the treatment of a variety of interpolation problems for nest algebras which have been considered recently in the literature. Applications include the treatment of robust control for time-varying systems.Partially supported by NSF grant DMS-9500912 相似文献
19.
Let T be an algebraically paranormal operator acting on Hilbert
space. We prove : (i) Weyls theorem holds for f(T) for every f $\in$ H((T));
(ii) a-Browders theorem holds for f(S) for every S $\prec$ T and f $\in$ H((S));
(iii) the spectral mapping theorem holds for the Weyl spectrum of T and for
the essential approximate point spectrum of T. 相似文献
20.
In this note we show that if either T or T* is totally *-paranormal
then Weyls theorem holds for f(T) for every f
, and also a-Weyls theorem holds for f(T) if T is totally *-paranormal. We prove that if either
T or T* is *-paranormal then the spectral mapping theorem holds for the
Weyl spectrum and for the essential approximate point spectrum. 相似文献