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1.
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   

2.
In this paper, we present a complement of a generalized Ando-Hiai inequality due to Fujii and Kamei [M. Fujii, E. Kamei, Ando-Hiai inequality and Furuta inequality, Linear Algebra Appl. 416 (2006) 541-545]. Let A and B be positive operators on a Hilbert space H such that 0<m1?A?M1 and 0<m2?B?M2 for some scalars mi?Mi (i=1,2), and let α∈[0,1]. Put for i=1,2. Then for each 0<r?1 and s?1
  相似文献   

3.
In this paper operator-valued Q-functions of Krein-Ovcharenko type are introduced. Such functions arise from the extension theory of Hermitian contractive operators A in a Hilbert space ℌ. The definition is related to the investigations of M.G. Krein and I.E. Ovcharenko of the so-called Qμ- and QM-functions. It turns out that their characterizations of such functions hold true only in the matrix valued case. The present paper extends the corresponding properties for wider classes of selfadjoint contractive extensions of A. For this purpose some peculiar but fundamental properties on the behaviour of operator ranges of positive operators will be used. Also proper characterizations for Qμ- and QM-functions in the general operator-valued case are given. Shorted operators and parallel sums of positive operators will be needed to give a geometric understanding of the function-theoretic properties of the corresponding Q-functions.  相似文献   

4.
Operators possessing analytic generalized inverses satisfying the resolvent identity are studied. Several characterizations and necessary conditions are obtained. The maximal radius of regularity for a Fredholm operatorT is computed in terms of the spectral radius of a generalized inverse ofT. This provides a partial answer to a conjecture of J. Zemánek.  相似文献   

5.
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   

6.
When AB(H) and BB(K) are given, we denote by MC the operator matrix acting on the infinite-dimensional separable Hilbert space HK of the form In this paper, for given A and B, the sets and ?C∈Inv(K,H)σl(MC) are determined, where σl(T),Bl(K,H) and Inv(K,H) denote, respectively, the left spectrum of an operator T, the set of all the left invertible operators and the set of all the invertible operators from K into H.  相似文献   

7.
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   

8.
We study finite dimensional perturbations of shift operators and their membership to the classes A m, n appearing in the theory of dual algebras. The results obtained yield informations about the lattice of invariant subspaces via the techniques of Scott Brown.  相似文献   

9.
Some sharp bounds for the Euclidean operator radius of two bounded linear operators in Hilbert spaces are given. Their connection with Kittaneh’s recent results which provide sharp upper and lower bounds for the numerical radius of linear operators are also established.  相似文献   

10.
11.
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   

12.
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   

13.
W. Kerscher  R. Nagel 《Acta Appl Math》1984,2(3-4):297-309
In this paper we survey the Perron-Frobenius spectral theory for positive semigroups on Banach lattices and indicate its applications to stability theory of retarded differential equations and quasi-periodic flows.  相似文献   

14.
Topological uniform descent and Weyl type theorem   总被引:1,自引:0,他引:1  
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   

15.
16.
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   

17.
Given a bounded linear operatorA in an infinite dimensional Banach space and a compact subset of a connected component of its semi-Fredholm domain, we construct a finite rank operatorF such that –A+F is bounded below (or surjective) for each ,F 2=0 and rankF=max min{dimN(–A), codimR(–A)}, if ind(–A)0 (or ind(–A)0, respectively) for each .  相似文献   

18.
A class of linear bounded staircase operators (H, G spaces) defined by (1) with two infinite sequences of orthogonal decompositions ofH and chain property (2) is considered. Necessary and sufficient conditions for the factorizationZ=XY are obtained, whereX, Y are block-diagonal, bounded, andY has a bounded inverse. All the pairs (X, Y) are explicitly constructed. These conditions are specialized for finite and infinite dimensions of the blocks ofX, Y and for differentX, Y. A direct application to bitriangular and biquasitriangular operators is indicated.  相似文献   

19.
Let T- S, be a family of not necessarily bounded semi-Fredholm operators, where T and S are operators acting between Banach spaces X and Y, and where S is bounded with D(S) D(T). For compact sets , as well as for certain open sets , we investigate existence and minimal rank of bounded feedback perturbations of the form F=BE such that min.ind (T-S+F)=0 for all . Here B is a given operator from a linear space Z to Y and E is some operator from X to Z.We give a simple characterization of that situation, when such regularizing feedback perturbations exist and show that for compact sets the minimal rank never exceeds max { min.ind (T-S) }+1. Moreover, an example shows that the minimal rank, in fact, may increase from max {...} to max {...}+1, if the given B enforces a certain structure of the feedbachk perturbation F.However, the minimal rank is equal to max { min.ind (T-S) }, if is an open set such that min.ind (T-S) already vanishes for all but finitely many points . We illustrate this result by applying it to the stabilization of certain infinite-dimensional dynamical systems in Hilbert space.  相似文献   

20.
On a class of quasi-Fredholm operators   总被引:1,自引:0,他引:1  
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   

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