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1.
Representations are given for the multiplicity of an analytic operator-valued function A at an isolated point z0 of the spectrum in the form of kernels and ranges of Hankel and Toeplitz matrices whose entries are derived from the Taylor coefficients of A and the Laurent coefficients of A−1 about z0. In two special cases the results can be expressed in terms of finite matrices: when A is a polynomial and when A−1 has a pole at z0. The latter case leads to the theory of Jordan chains. 相似文献
2.
Michael Gil’ 《Quaestiones Mathematicae》2016,39(2):145-152
Let SNr (r ≥ 1) denote the Schatten-von Neumann ideal of compact operators in a separable Hilbert space. For the block matrixthe inequality(p = 2; 3;?…?) is proved, where λk(A) (k = 1; 2;?…?) are the eigenvalues of A and Nr(.) is the norm in SNr. Moreover, let P(z) = z2I + Bz + C (z ∈ ?) with B ∈ SN2p, C ∈ SNp. By zk(P) (k = 1; 2;?…?) the characteristic values of the pencil P are denoted. It is shown thatIn the case p = 1, sharper results are established. In addition, it is derived that 相似文献
3.
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
4.
Israel Feldman 《Integral Equations and Operator Theory》1993,16(3):385-391
Sufficient conditions are given for the finiteness of the discrete spectrum of the block Toeplitz operatorT
A generated in the spaceH
2
n
by self-adjoint matrix functionA(t)(|t|=1). These results are obtained by means of theorems concerning the spectrum of a perturbed self-adjoint operators. 相似文献
5.
This paper mainly considers Toeplitz algebras, subnormal tuples and rigidity concerning reproducing C[z1,…,zd]-modules. By making use of Arveson's boundary representation theory, we find there is more rigidity in several variables than there is in single variable. We specialize our attention to reproducing C[z1,…,zd]-modules with -invariant kernels by examining the spectrum and the essential spectrum of the d-tuple {Mz1,…,Mzd}, and deducing an exact sequence of C∗-algebras associated with Toeplitz algebra. Finally, we deal with Toeplitz algebras defined on Arveson submodules and rigidity of Arveson submodules. 相似文献
6.
Jörg Eschmeier 《Mathematische Annalen》2007,339(1):21-35
In this note we combine methods from commutative algebra and complex analytic geometry to calculate the generic values of
the cohomology dimensions of a commuting multioperator on its Fredholm domain. More precisely, we prove that, for a given
Fredholm tuple T = (T
1, ..., T
n
) of commuting bounded operators on a complex Banach space X, the limits exist and calculate the generic dimension of the cohomology groups H
p
(z − T, X) of the Koszul complex of T near z = 0. To deduce this result we show that the above limits coincide with the Samuel multiplicities of the stalks of the cohomology
sheaves of the associated complex of analytic sheaves at z = 0. 相似文献
7.
Suppose that {D
n
} is a sequence of invertible operators on a Hilbert space, andD
n
T D
n
–1
converges in norm toT
0. Recently, H. Bercovici, C. Foias, and A. Tannenbaum have shown that if {D
n
±1
n=1, 2,...} is contained in a finite dimensional subspace of operators, thenT andT
0 must have the same spectral radius. Using this result, R. Teodorescu proved that the resolvents ofT andT
0 have the same unbounded component. We show that in fact the spectra differ only by certain eigenvalues ofT
0, and the spectrum ofT
0 is obtained by filling in holes in the spectrum ofT; i.e., by adjoining (all, some, or none of the) bounded components of the resolvent ofT to the spectrum ofT. 相似文献
8.
J. J. Koliha 《Aequationes Mathematicae》1977,16(1-2):31-35
The paper gives a necessary and sufficient condition on the spectrum of a bounded linear operator on Banach space for the convergence of the series
0
T(I-T
2)
n
. Some properties of the sum are investigated. 相似文献
9.
A complex number λ is an extended eigenvalue of an operator A if there is a nonzero operator X such that AX = λ XA. We characterize the set of extended eigenvalues, which we call extended point spectrum, for operators acting on finite dimensional
spaces, finite rank operators, Jordan blocks, and C0 contractions. We also describe the relationship between the extended eigenvalues of an operator A and its powers. As an application, we show that the commutant of an operator A coincides with that of An, n ≥ 2, n ∈ N if the extended point spectrum of A does not contain any n–th root of unity other than 1. The converse is also true if either A or A* has trivial kernel. 相似文献
10.
Erwann Delay 《manuscripta mathematica》2007,123(2):147-165
Let (M =]0, ∞[×N, g) be an asymptotically hyperbolic manifold of dimension n + 1 ≥ 3, equipped with a warped product metric. We show that there exist no TT L
2-eigentensors with eigenvalue in the essential spectrum of the Lichnerowicz Laplacian Δ
L
. If (M, g) is the real hyperbolic space, there is no symmetric L
2-eigentensors of Δ
L
. 相似文献
11.
Oscar F. Bandtlow 《Integral Equations and Operator Theory》2008,61(1):21-43
For a, α > 0 let E(a, α) be the set of all compact operators A on a separable Hilbert space such that s
n
(A) = O(exp(-anα)), where s
n
(A) denotes the n-th singular number of A. We provide upper bounds for the norm of the resolvent (zI − A)−1 of A in terms of a quantity describing the departure from normality of A and the distance of z to the spectrum of A. As a consequence we obtain upper bounds for the Hausdorff distance of the spectra of two operators in E(a, α).
相似文献
12.
Onur Yavuz 《Integral Equations and Operator Theory》2007,58(3):433-446
We consider a multiply connected domain
where
denotes the unit disk and
denotes the closed disk centered at
with radius r
j
for j = 1, . . . , n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains ∂Ω and does not contain the points λ1, λ2, . . . , λ
n
, and the operators T and r
j
(T − λ
j
I)−1 are polynomially bounded, then there exists a nontrivial common invariant subspace for T
* and (T − λ
j
I)*-1. 相似文献
13.
Bao Qin Li 《Mathematische Zeitschrift》2008,258(4):763-771
We show that meromorphic solutions f, g of f
2 + g
2 = 1 in C2 must be constant, if f
z2 and g
z1 have the same zeros (counting multiplicities). We also apply the result to characterize meromorphic solutions of certain
nonlinear partial differential equations. 相似文献
14.
D. S. Kalyuzhniy-Verbovetzky 《Integral Equations and Operator Theory》2002,43(4):450-465
We prove that an arbitrary function, which is holomorphic on some neighbourhood ofz=0 in
N
and vanishes atz=0, and whose values are bounded linear operators mapping one separable Hilbert space into another one, can be represented as the transfer function of some multi-parameter discrete time-invariant conservative scattering linear system whose state space is a Krein space.The author is thankful to Prof. D.Z. Arov for suggesting this problem. He wishes also to thank Leeds University, where the revised version of this paper was prepared, for its hospitality, and Dr. V.V. Kisil who organized his visit there under the International Short Visits Scheme of LMS (grant no. 5620). 相似文献
15.
《Quaestiones Mathematicae》2013,36(3):413-422
AbstractIn this paper, we characterize the Taylor spectrum for a certain class of commuting n-contractions. We also investigate the behavior of this spectrum under action of involutive automorphisms of the unit ball 𝔹 n. 相似文献
16.
Heinz Langer Alexander Markus Vladimir Matsaev 《Integral Equations and Operator Theory》2009,63(4):533-545
In this note we continue the study of spectral properties of a self-adjoint analytic operator function A(z) that was started in [5]. It is shown that if A(z) satisfies the Virozub–Matsaev condition on some interval Δ0 and is boundedly invertible in the endpoints of Δ0, then the ‘embedding’ of the original Hilbert space into the Hilbert space , where the linearization of A(z) acts, is in fact an isomorphism between a subspace of and . As a consequence, properties of the local spectral function of A(z) on Δ0 and a so-called inner linearization of the operator function A(z) in the subspace are established.
相似文献
17.
B. Yousefi 《Archiv der Mathematik》2004,83(6):536-539
Let
be a Hilbert space of functions analytic on a plane domain such that for every in the functional of evaluation at is bounded. Assume further that
contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.Received: 17 February 2004 相似文献
18.
19.
Estimates for the zeros of differences of meromorphic functions 总被引:6,自引:0,他引:6
SHON Kwang Ho 《中国科学A辑(英文版)》2009,52(11):2447-2458
Let f be a transcendental meromorphic function and g(z)=f(z+c1)+f(z+c2)-2f(z) and g2(z)=f(z+c1)·f(z+c2)-f2(z).The exponents of convergence of zeros of differences g(z),g2(z),g(z)/f(z),and g2(z)/f2(z) are estimated accurately. 相似文献
20.
Wen Zhang 《Linear algebra and its applications》2011,435(6):1326-1335
Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y, respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is the set σπ(A)={z∈σ(A):|z|=maxω∈σ(A)|ω|}, where σ(A) denotes the spectrum of A. Assume that Φ:A→B is a map the range of which contains all operators of rank at most two. It is shown that the map Φ satisfies the condition that σπ(BAB)=σπ(Φ(B)Φ(A)Φ(B)) for all A,B∈A if and only if there exists a scalar λ∈C with λ3=1 and either there exists an invertible operator T∈B(X,Y) such that Φ(A)=λTAT-1 for every A∈A; or there exists an invertible operator T∈B(X∗,Y) such that Φ(A)=λTA∗T-1 for every A∈A. If X=H and Y=K are complex Hilbert spaces, the maps preserving the peripheral spectrum of the Jordan skew semi-triple product BA∗B are also characterized. Such maps are of the form A?UAU∗ or A?UAtU∗, where U∈B(H,K) is a unitary operator, At denotes the transpose of A in an arbitrary but fixed orthonormal basis of H. 相似文献