共查询到20条相似文献,搜索用时 31 毫秒
1.
For any operator A on a Hilbert space, let W(A), w(A) and w0(A) denote its numerical range, numerical radius and the distance from the origin to the boundary of its numerical range, respectively. We prove that if An=0, then w(A)?(n-1)w0(A), and, moreover, if A attains its numerical radius, then the following are equivalent: (1) w(A)=(n-1)w0(A), (2) A is unitarily equivalent to an operator of the form aAn⊕A′, where a is a scalar satisfying |a|=2w0(A), An is the n-by-n matrix
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3.
B.P. Duggal 《Linear algebra and its applications》2007,422(1):331-340
A Hilbert space operator A ∈ B(H) is said to be p-quasi-hyponormal for some 0 < p ? 1, A ∈ p − QH, if A∗(∣A∣2p − ∣A∗∣2p)A ? 0. If H is infinite dimensional, then operators A ∈ p − QH are not supercyclic. Restricting ourselves to those A ∈ p − QH for which A−1(0) ⊆ A∗-1(0), A ∈ p∗ − QH, a necessary and sufficient condition for the adjoint of a pure p∗ − QH operator to be supercyclic is proved. Operators in p∗ − QH satisfy Bishop’s property (β). Each A ∈ p∗ − QH has the finite ascent property and the quasi-nilpotent part H0(A − λI) of A equals (A − λI)-1(0) for all complex numbers λ; hence f(A) satisfies Weyl’s theorem, and f(A∗) satisfies a-Weyl’s theorem, for all non-constant functions f which are analytic on a neighborhood of σ(A). It is proved that a Putnam-Fuglede type commutativity theorem holds for operators in p∗ − QH. 相似文献
4.
Let W and M be two finite dimensional subspaces of a Hilbert space H such that H=W⊕M⊥, and let PW‖M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of PW‖M⊥
5.
B.P. Duggal 《Linear algebra and its applications》2008,428(4):1109-1116
A Hilbert space operator A∈B(H) is p-hyponormal, A∈(p-H), if |A∗|2p?|A|2p; an invertible operator A∈B(H) is log-hyponormal, A∈(?-H), if log(TT∗)?log(T∗T). Let dAB=δAB or ?AB, where δAB∈B(B(H)) is the generalised derivation δAB(X)=AX-XB and ?AB∈B(B(H)) is the elementary operator ?AB(X)=AXB-X. It is proved that if A,B∗∈(?-H)∪(p-H), then, for all complex λ, , the ascent of (dAB-λ)?1, and dAB satisfies the range-kernel orthogonality inequality ‖X‖?‖X-(dAB-λ)Y‖ for all X∈(dAB-λ)-1(0) and Y∈B(H). Furthermore, isolated points of σ(dAB) are simple poles of the resolvent of dAB. A version of the elementary operator E(X)=A1XA2-B1XB2 and perturbations of dAB by quasi-nilpotent operators are considered, and Weyl’s theorem is proved for dAB. 相似文献
6.
Kazuyoshi Okubo 《Linear algebra and its applications》2006,419(1):48-52
Let T∈B(H) be an invertible operator with polar decomposition T = UP and B∈B(H) commute with T. In this paper we prove that ∣∣∣PλBUP1−λ∣∣∣ ? ∣∣∣BT∣∣∣, where ∣∣∣ · ∣∣∣ is a weakly unitarily invariant norm on B(H) and 0 ? λ ? 1. As the consequence of this result, we have ∣∣∣f(PλUP1−λ)∣∣∣ ? ∣∣∣f(T)∣∣∣ for any polynomial f. 相似文献
7.
Mouez Dimassi 《Journal of Functional Analysis》2005,225(1):193-228
We study the spectral shift function s(λ,h) and the resonances of the operator P(h)=-Δ+V(x)+W(hx). Here V is a periodic potential, W a decreasing perturbation and h a small positive constant. We give a representation of the derivative of s(λ,h) related to the resonances of P(h), and we obtain a Weyl-type asymptotics of s(λ,h). We establish an upper bound O(h-n+1) for the number of the resonances of P(h) lying in a disk of radius h. 相似文献
8.
For a finite-dimensional linear subspace S⊆L(V,W) and a positive integer k, the k-reflexivity defect of S is defined by rdk(S)=dim(Refk(S)/S), where Refk(S) is the k-reflexive closure of S. We study this quantity for two-dimensional spaces of operators and for single generated algebras and their commutants. 相似文献
9.
Maria Inez Cardoso Gonçalves Ahmed Ramzi Sourour 《Linear algebra and its applications》2008,429(7):1478-1488
For 0<q<1, the q-numerical range is defined on the algebra Mn of all n×n complex matrices by
Wq(A)={x∗Ay:x,y∈Cn,∥x∥=∥y∥=1,〈y,x〉=q}. 相似文献
10.
Maps completely preserving spectral functions 总被引:1,自引:0,他引:1
Let X,Y be infinite dimensional complex Banach spaces and A,B be standard operator algebras on X and Y, respectively. In this paper, we show that surjective maps completely preserving certain spectral function Δ(·) from A to B are isomorphisms, where Δ(·) stands for any one of 13 spectral functions σ(·), σl(·), σr(·), σl(·)∩σr(·), ∂σ(·), ησ(·), σp(·), σc(·), σp(·)∩σc(·), σp(·)∪σc(·), σap(·), σs(·), and σap(·)∩σs(·). 相似文献
11.
S.W. Drury 《Linear algebra and its applications》2011,435(2):323-329
We present an effective algorithm for estimating the norm of an operator mapping a low-dimensional ?p space to a Banach space with an easily computable norm. We use that algorithm to show that Matsaev’s proposed extension of the inequality of John von Neumann is false in case p=4. Matsaev conjectured that for every contraction T on Lp (1<p<∞) one has for any polynomial P
‖P(T)‖Lp→Lp?‖P(S)‖?p(Z+)→?p(Z+) 相似文献
12.
Jon Wilkening 《Linear algebra and its applications》2007,427(1):6-25
We present an efficient algorithm for obtaining a canonical system of Jordan chains for an n × n regular analytic matrix function A(λ) that is singular at the origin. For any analytic vector function b(λ), we show that each term in the Laurent expansion of A(λ)−1b(λ) may be obtained from the previous terms by solving an (n + d) × (n+d) linear system, where d is the order of the zero of det A(λ) at λ = 0. The matrix representing this linear system contains A(0) as a principal submatrix, which can be useful if A(0) is sparse. The last several iterations can be eliminated if left Jordan chains are computed in addition to right Jordan chains. The performance of the algorithm in floating point and exact (rational) arithmetic is reported for several test cases. The method is shown to be forward stable in floating point arithmetic. 相似文献
13.
Let Mn be the algebra of all n×n matrices, and let φ:Mn→Mn be a linear mapping. We say that φ is a multiplicative mapping at G if φ(ST)=φ(S)φ(T) for any S,T∈Mn with ST=G. Fix G∈Mn, we say that G is an all-multiplicative point if every multiplicative linear bijection φ at G with φ(In)=In is a multiplicative mapping in Mn, where In is the unit matrix in Mn. We mainly show in this paper the following two results: (1) If G∈Mn with detG=0, then G is an all-multiplicative point in Mn; (2) If φ is an multiplicative mapping at In, then there exists an invertible matrix P∈Mn such that either φ(S)=PSP-1 for any S∈Mn or φ(T)=PTtrP-1 for any T∈Mn. 相似文献
14.
Andrew Hassell 《Advances in Mathematics》2008,217(2):586-682
Consider a compact manifold with boundary M with a scattering metric g or, equivalently, an asymptotically conic manifold (M○,g). (Euclidean Rn, with a compactly supported metric perturbation, is an example of such a space.) Let Δ be the positive Laplacian on (M,g), and V a smooth potential on M which decays to second order at infinity. In this paper we construct the kernel of the operator −1(h2Δ+V−2(λ0±i0)), at a non-trapping energy λ0>0, uniformly for h∈(0,h0), h0>0 small, within a class of Legendre distributions on manifolds with codimension three corners. Using this we construct the kernel of the propagator, e−it(Δ/2+V), t∈(0,t0) as a quadratic Legendre distribution. We also determine the global semiclassical structure of the spectral projector, Poisson operator and scattering matrix. 相似文献
15.
Fernando De Terán 《Linear algebra and its applications》2010,432(4):892-910
We develop first order eigenvalue expansions of one-parametric perturbations of square singular matrix polynomials. Although the eigenvalues of a singular matrix polynomial P(λ) are not continuous functions of the entries of the coefficients of the polynomial, we show that for most perturbations they are indeed continuous. Given an eigenvalue λ0 of P(λ) we prove that, for generic perturbations M(λ) of degree at most the degree of P(λ), the eigenvalues of P(λ)+?M(λ) admit covergent series expansions near λ0 and we describe the first order term of these expansions in terms of M(λ0) and certain particular bases of the left and right null spaces of P(λ0). In the important case of λ0 being a semisimple eigenvalue of P(λ) any bases of the left and right null spaces of P(λ0) can be used, and the first order term of the eigenvalue expansions takes a simple form. In this situation we also obtain the limit vector of the associated eigenvector expansions. 相似文献
16.
Artur Bartoszewicz Artur Wachowicz 《Journal of Mathematical Analysis and Applications》2011,375(2):431-435
We answer the questions asked by Faisant et al. (2005) [2]. The first main result states that for every admissible ideal I⊂P(N) the quotient space l∞(I)/c0(I) is complete. The second main result states that consistently there is an admissible ideal I⊂P(N) such that the sets W(I), of all real sequences with finite I-variation, and c?(I), of all restrictively I-convergent sequences, are equal. 相似文献
17.
We prove that the operator G, the closure of the first-order differential operator −d/dt+D(t) on L2(R,X), is Fredholm if and only if the not well-posed equation u′(t)=D(t)u(t), t∈R, has exponential dichotomies on R+ and R− and the ranges of the dichotomy projections form a Fredholm pair; moreover, the index of this pair is equal to the Fredholm index of G. Here X is a Hilbert space, D(t)=A+B(t), A is the generator of a bi-semigroup, B(⋅) is a bounded piecewise strongly continuous operator-valued function. Also, we prove some perturbations results and consider various examples of not well-posed problems. 相似文献
18.
Pl. Muthuramalingam 《Mathematische Nachrichten》1986,127(1):145-163
We prove asymptotic completeness using ENSS' method for h0(P) + WS(Q) + WL(Q) where h0: Rn → R is a polynomial of degree 2 with lim lim|ξ|→∞h0(ξ)| + |Δh0(ξ)| = ∞, WS a short range potential and WL a smooth long range potential. 相似文献
19.
Let T be a linear bounded cyclic operator in a separable complex Hilbert space H. Let B(T) and Ba(T) denote, respectively, the set of bounded point evaluation and the set of analytic point evaluation of T. We show that if T has the Bishop property (β), then Ba(T)=B(T)?σap(T), where σap(T) is the approximate spectrum of T. In the particular case when T is an operator of multiplication by z in a Hardy space this was proved by Trent (Pacific J. Math. 80 (1979) 279). On the other hand, using the generalized and the local spectral theory we obtain sufficient conditions on Ba(T) under which the spectrum of T and the local spectrum of T at any y≠0 in H coincide. At the end results involving the spectral picture of quasi-similar cyclic operators are given. 相似文献
20.
W. Arendt 《Journal of Differential Equations》2011,251(8):2100-2124
We consider a bounded connected open set Ω⊂Rd whose boundary Γ has a finite (d−1)-dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operator D0 on L2(Γ) by form methods. The operator −D0 is self-adjoint and generates a contractive C0-semigroup S=(St)t>0 on L2(Γ). We show that the asymptotic behaviour of St as t→∞ is related to properties of the trace of functions in H1(Ω) which Ω may or may not have. 相似文献