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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.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
Yu. M. Arlinskii S. Hassi H. S. V. de Snoo 《Integral Equations and Operator Theory》2005,53(2):153-189
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
9.
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
11.
Scott McCullough 《Integral Equations and Operator Theory》1996,25(1):104-127
For the special case of a Riemann surface which arises as the double of a planar domainR, the trisecant identity has a natural interpretation as a relation among reproducing kernels for subspaces of the Hardy spaceH
2
(R). This relation and Riemann's theorem on the vanishing of the theta function is applied to Nevanlinna-Pick interpolation onR. 相似文献
12.
A bounded linear operator T ∈ L(X) on aBanach space X is said to satisfy “Browder’s theorem” if the Browder spectrum coincides with the Weyl spectrum. T ∈ L(X) is said to satisfy “a-Browder’s theorem” if the upper semi-Browder spectrum coincides with the approximate point Weyl spectrum. In this note we give several characterizations of operators satisfying these theorems. Most of these characterizations are obtained by using a localized version of the single-valued extension property of T. In the last part we shall give some characterizations of operators for which “Weyl’s theorem” holds. 相似文献
13.
When A∈B(H) and B∈B(K) are given, we denote by MC the operator matrix acting on the infinite-dimensional separable Hilbert space H⊕K 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
14.
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
15.
Given a convex domain
with conic boundary, a linear operator A with numerical range contained in Ω, and a rational function bounded on Ω, we are interested in estimating the norm of r(A) in terms of the supremum of r in Ω. In particular, we show that ellipses, hyperbolas and parabolas are K-spectral sets with
.
Received: 22 December 2005 Revised: 11 September 2006 相似文献
16.
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
17.
We study finite rank perturbations of contractions of classC
.0 with finite defect indices. The completely nonunitary part of such a perturbation is also of classC
.0, while the unitary part is singular. When the defect indices of the original contraction are not equal, it can be shown that almost always (with respect to a suitable measure) the perturbation has no unitary part. 相似文献
18.
Dijana Mosi? 《Linear algebra and its applications》2010,432(11):2847-1417
In this paper we prove the formula for the expression (A+B)d,W in terms of A,B,W,Ad,W,Bd,W, assuming some conditions for A,B and W. Here Sd,W denotes the generalized W-weighted Drazin inverse of a linear bounded operator S on a Banach space. 相似文献
19.
Jean-Christophe Bourin 《Linear algebra and its applications》2006,413(1):212-217
We review some recent convexity results for Hermitian matrices and we add a new one to the list: Let A be semidefinite positive, let Z be expansive, Z∗Z?I, and let f:[0,∞)→[0,∞) be a concave function. Then, for all symmetric norms
‖f(Z∗AZ)‖?‖Z∗f(A)Z‖. 相似文献
20.
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