共查询到20条相似文献,搜索用时 31 毫秒
1.
We use a recent result concerning the eigenvalues of a generic (non-Hermitian) complex perturbation of a bounded Hermitian sequence of matrices to prove that the asymptotic spectrum of the product of Toeplitz sequences, whose symbols have a real-valued essentially bounded product h, is described by the function h in the “Szegö way”. Then, using Mergelyan’s theorem, we extend the result to the more general case where h belongs to the Tilli class. The same technique gives us the analogous result for sequences belonging to the algebra generated by Toeplitz sequences, if the symbols associated with the sequences are bounded and the global symbol h belongs to the Tilli class. A generalization to the case of multilevel matrix-valued symbols and a study of the case of Laurent polynomials not necessarily belonging to the Tilli class are also given. 相似文献
2.
udy the perturbation theory of structured matrices under structured rank one perturbations, and then focus on several classes of complex matrices. Generic Jordan structures of perturbed matrices are identified. It is shown that the perturbation behavior of the Jordan structures in the case of singular J-Hamiltonian matrices is substantially different from the corresponding theory for unstructured generic rank one perturbation as it has been studied in [18, 28, 30, 31]. Thus a generic structured perturbation would not be generic if considered as an unstructured perturbation. In other settings of structured matrices, the generic perturbation behavior of the Jordan structures, within the confines imposed by the structure, follows the pattern of that of unstructured perturbations. 相似文献
3.
Jorge Antezana Gustavo Corach Demetrio Stojanoff 《Integral Equations and Operator Theory》2006,55(2):169-188
If
$$\mathcal{H}$$ is a Hilbert space,
$$\mathcal{S}$$ is a closed subspace of
$$\mathcal{H},$$ and A is a positive bounded linear operator on
$$\mathcal{H},$$ the spectral shorted operator
$$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ is defined as the infimum of the sequence
$$\sum (\mathcal{S},A^n )^{1/n} ,$$ where denotes
$$\sum \left( {\mathcal{S},B} \right)$$ the shorted operator of B to
$$\mathcal{S}.$$ We characterize the left spectral resolution of
$$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ and show several properties of this operator, particularly in the case that
dim
$${\mathcal{S} = 1.}$$ We use these results to generalize the concept of Kolmogorov complexity for the infinite dimensional
case and for non invertible operators. 相似文献
4.
Shanli Sun 《Linear algebra and its applications》2010,433(4):737-749
In this paper, the concept of generalized hermitian operators defined on a complex Hilbert space is introduced. It is shown that the spectrums and the Fredholm fields of generalized hermitian operators are both symmetric with respect to the real axis. Some other results on generalized hermitian operators are obtained. 相似文献
5.
Special classes of functions on the classical semigroupN of non-negative integers, as defined using the classical backward and forward difference operators, get associated in a natural way with special classes of bounded linear operators on Hilbert spaces. In particular, the class of completely monotone functions, which is a subclass of the class of positive definite functions ofN, gets associated with subnormal operators, and the class of completely alternating functions, which is a subclass of the class of negative definite functions onN, with completely hyper-expansive operators. The interplay between the theories of completely monotone and completely alternating functions has previously been exploited to unravel some interesting connections between subnormals and completely hyperexpansive operators. For example, it is known that a completely hyperexpansive weighted shift with the weight sequence {n}(n0) (of positive reals) gives rise to a subnormal weighted shift whose weight sequence is {1/n}(n0). The present paper discovers some new connections between the two classes of operators by building upon some well-known results in the literature that relate positive and negative definite functions on cartesian products of arbitrary sets using Bernstein functions. In particular, it is observed that the weight sequence of a completely hyperexpansive weighted shift with the weight sequence {n}(n0) (of positive reals) gives rise to a subnormal weighted shift whose weight sequence is {n+1/n}(n0). It is also established that the weight sequence of any completely hyperexpansive weighted shift is a Hausdorff moment sequence. Further, the connection of Bernstein functions with Stieltjes functions and generalizations thereof is exploited to link certain classes of subnormal weighted shifts to completely hyperexpansive ones. 相似文献
6.
We prove a stability theorem for the eigenvalues of general non-negative self-adjoint linear operators with compact resolvents and by applying it we prove a sharp stability result for the dependence of the eigenvalues of second order uniformly elliptic linear operators with homogeneous Neumann boundary conditions upon domain perturbation. 相似文献
7.
Victor I. Burenkov 《Journal of Differential Equations》2008,244(7):1712-1740
We prove sharp stability results for the dependence of the eigenvalues of second order uniformly elliptic linear operators with homogeneous Dirichlet boundary conditions upon domain perturbation. 相似文献
8.
9.
In this note we give an example of an ∞-hyponormal operator T whose Aluthge transform
is not (1+ɛ)-hyponormal for any ɛ > 0 and show that the sequence
of interated Aluthge transforms of T need not converge in the weak operator topology, which solve two problems in [6]. 相似文献
10.
Matjaž Konvalinka 《Integral Equations and Operator Theory》2005,52(2):271-284
An operator on a complex Banach space is polynomially compact if a non-zero polynomial of the operator is compact, and power compact if a power of the operator is compact. Theorems on triangularizability of algebras (resp. semigroups) of compact operators are shown to be valid also for algebras (resp. semigroups) of polynomially (resp. power) compact operators, provided that pairs of operators have compact commutators. 相似文献
11.
We give a matrix version of the scalar inequality f(a + b) ? f(a) + f(b) for positive concave functions f on [0, ∞). We show that Choi’s inequality for positive unital maps and operator convex functions remains valid for monotone convex functions at the cost of unitary congruences. Some inequalities for log-convex functions are presented and a new arithmetic-geometric mean inequality for positive matrices is given. We also point out a simple proof of the Bhatia-Kittaneh arithmetic-geometric mean inequality. 相似文献
12.
A bi-infinite sequence ...,t
–2,t
–1,t
0,t
1,t
2,... of nonnegativep×p matrices defines a sequence of block Toeplitz matricesT
n
=(t
ik
),n=1,2,...,, wheret
ik
=t
k–i
,i,k=1,...,n. Under certain irreducibility assumptions, we show that the limit of the spectral radius ofT
n
, asn tends to infinity, is given by inf{()[0,]}, where () is the spectral radius of
jz
t
j
j
.Supported by SFB 343 Diskrete Strukturen in der Mathematik, Universität Bielefeld 相似文献
13.
Jürgen Voigt 《Acta Appl Math》1984,2(3-4):311-331
We present methods using positive semigroups and perturbation theory in the application to the linear Boltzmann equation. Besides being a review, this paper also presents generalizations of known results and develops known methods in a more abstract setting.In Section 1 we present spectral properties of the semigroup operatorsW
a(t) of the absorption semigroup and its generatorT
a. In Section 2 we treat the full semigroup (W(t);t0) as a perturbation of the absorption semigroup. We discuss part of the problems (perturbation arguments and existence of eigenvalues) which have to be solved in order to obtain statements about the large time behaviour ofW(·). In Section 3 we discuss irreducibility ofW(·).In four appendices we present abstract methods used in Sections 1, 2 and 3. 相似文献
14.
Qianglian Huang 《Linear algebra and its applications》2011,434(12):2468-2474
The main concern of this paper is the perturbation problem for oblique projection generalized inverses of closed linear operators in Banach spaces. We provide a new stability characterization of oblique projection generalized inverses of closed linear operators under T-bounded perturbations, which improves some well known results in the case of the closed linear operators under the bounded perturbation or that the perturbation does not change the null space. 相似文献
15.
Let T be a completely nonunitary contraction on a Hilbert space H with r(T)=1. Let an>0, an→0. Then there exists x∈H with |〈Tnx,x〉|?an for all n. We construct a unitary operator without this property. This gives a negative answer to a problem of van Neerven. 相似文献
16.
Tetsuo Harada 《Linear algebra and its applications》2007,425(1):102-108
Let A and B be invertible positive elements in a II1-factor A, and let μs(·) be the singular number on A. We prove that
exp∫Klogμs(AB)ds?exp∫Ilogμs(A)ds·exp∫Jlogμs(B)ds, 相似文献
17.
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
18.
V. Kostrykin K. A. Makarov A. K. Motovilov 《Integral Equations and Operator Theory》2005,51(1):121-140
Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d > 0 be the distance between the spectra of A and C. Under these assumptions we prove that the best possible value of the constant c in the condition
guaranteeing the existence of a (bounded) solution to the operator Riccati equation XA–CX+XBX = B* is equal to
We also prove an extension of the Davis-Kahan tan theorem and provide a sharp estimate for the norm of the solution to the Riccati equation. If C is bounded, we prove, in addition, that the solution X is a strict contraction if B satisfies the condition
and that this condition is optimal. 相似文献
19.
Spectral pictures of Aluthge transforms of operators 总被引:4,自引:0,他引:4
In this paper we continue our study, begun in [12], of the relationships between an arbitrary operatorT on Hilbert space and its Aluthge transform
. In particular, we show that in most cases the spectral picture ofT coincides with that of
, and we obtain some interesting connections betweenT and
as a consequence. 相似文献
20.
Aluthge transforms of operators 总被引:7,自引:0,他引:7
Associated with every operatorT on Hilbert space is its Aluthge transform
(defined below). In this note we study various connections betweenT and
, including relations between various spectra, numerical ranges, and lattices of invariant subspaces. In particular, we show that if
has a nontrivial invariant subspace, then so doesT, and we give various applications of our results. 相似文献