共查询到20条相似文献,搜索用时 15 毫秒
1.
Marek Niezgoda 《Linear algebra and its applications》2010,433(1):136-640
Let a,b>0 and let Z∈Mn(R) such that Z lies into the operator ball of diameter [aI,bI]. Then for all positive definite A∈Mn(R),
2.
Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices
Chi-Kwong Li 《Linear algebra and its applications》2009,430(7):1739-1398
Let be the set of entrywise nonnegative n×n matrices. Denote by r(A) the spectral radius (Perron root) of . Characterization is obtained for maps such that r(f(A)+f(B))=r(A+B) for all . In particular, it is shown that such a map has the form
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4.
Let A be a unilateral (resp., bilateral) weighted shift with weights wn, n?0 (resp., −∞<n<∞). Eckstein and Rácz showed before that A has its numerical range W(A) contained in the closed unit disc if and only if there is a sequence (resp., ) in [−1,1] such that 2|wn|=(1−an)(1+an+1) for all n. In terms of such an?s, we obtain a necessary and sufficient condition for W(A) to be open. If the wn?s are periodic, we show that the an?s can also be chosen to be periodic. As a result, we give an alternative proof for the openness of W(A) for an A with periodic weights, which was first proven by Stout. More generally, a conjecture of his on the openness of W(A) for A with split periodic weights is also confirmed. 相似文献
5.
Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras 总被引:1,自引:0,他引:1
A nonlinear map φ between operator algebras is said to be a numerical radius isometry if w(φ(T−S))=w(T−S) for all T, S in its domain algebra, where w(T) stands for the numerical radius of T. Let and be two atomic nests on complex Hilbert spaces H and K, respectively. Denote the nest algebra associated with and the diagonal algebra. We give a thorough classification of weakly continuous numerical radius isometries from onto and a thorough classification of numerical radius isometries from onto . 相似文献
6.
Let 1 ? p ? ∞, 0 < q ? p, and A = (an,k)n,k?0 ? 0. Denote by Lp,q(A) the supremum of those L satisfying the following inequality:
7.
In this paper, we reconsider the iterative method Xk=Xk−1+βY(I−AXk−1), k=1,2,…,β∈C?{0} for computing the generalized inverse over Banach spaces or the generalized Drazin inverse ad of a Banach algebra element a, reveal the intrinsic relationship between the convergence of such iterations and the existence of or ad, and present the error bounds of the iterative methods for approximating or ad. Moreover, we deduce some necessary and sufficient conditions for iterative convergence to or ad. 相似文献
8.
Matthew Boylan 《Journal of Number Theory》2003,98(2):377-389
Let F(z)=∑n=1∞a(n)qn denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that
9.
S.W. Drury 《Linear algebra and its applications》2007,422(1):318-325
We establish the following case of the Determinantal Conjecture of Marcus [M. Marcus, Derivations, Plücker relations and the numerical range, Indiana Univ. Math. J. 22 (1973) 1137-1149] and de Oliveira [G.N. de Oliveira, Research problem: Normal matrices, Linear and Multilinear Algebra 12 (1982) 153-154]. Let A and B be unitary n × n matrices with prescribed eigenvalues a1, … , an and b1, … , bn, respectively. Then for any scalars t and s
10.
Consider an operator T:C2(R)→C(R) and isotropic maps A1,A2:C1(R)→C(R) such that the functional equation
11.
M. Anoussis 《Advances in Mathematics》2004,188(2):425-443
Let G be a compact group, not necessarily abelian, let ? be its unitary dual, and for f∈L1(G), let fn?f∗?∗f denote n-fold convolution of f with itself and f? the Fourier transform of f. In this paper, we derive the following spectral radius formula
12.
Let Mn(R) be the linear space of all n×n matrices over the real field R. For any A∈Mn(R), let ρ(A) and ‖A‖∞ denote the spectral radius and the infinity norm of A, respectively. By introducing a class of transformations φa on Mn(R), we show that, for any A∈Mn(R), ρ(A)<‖A‖∞ if . If A∈Mn(R) is nonnegative, we prove that ρ(A)<‖A‖∞ if and only if , and ρ(A)=‖A‖∞ if and only if the transformation φ‖A‖∞ preserves the spectral radius and the infinity norm of A. As an application, we investigate a class of linear discrete dynamic systems in the form of X(k+1)=AX(k). The asymptotical stability of the zero solution of the system is established by a simple algebraic method. 相似文献
13.
Hwa-Long Gau 《Linear algebra and its applications》2010,432(5):1310-1321
In this paper, we show that a reducible companion matrix is completely determined by its numerical range, that is, if two reducible companion matrices have the same numerical range, then they must equal to each other. We also obtain a criterion for a reducible companion matrix to have an elliptic numerical range, put more precisely, we show that the numerical range of an n-by-n reducible companion matrix C is an elliptic disc if and only if C is unitarily equivalent to A⊕B, where A∈Mn-2, B∈M2 with σ(B)={aω1,aω2}, , ω1≠ω2, and . 相似文献
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15.
Aljoša Peperko 《Linear algebra and its applications》2011,435(4):902-907
Given a bounded set Ψ of n×n non-negative matrices, let ρ(Ψ) and μ(Ψ) denote the generalized spectral radius of Ψ and its max version, respectively. We show that
16.
For finite subsets A1,…,An of a field, their sumset is given by . In this paper, we study various restricted sumsets of A1,…,An with restrictions of the following forms:
17.
In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))n?0 and (U(n))n?0, which are ultimately periodic modulo m, e.g.
18.
Zhi-Hong Sun 《Journal of Number Theory》2008,128(5):1295-1335
Let be a prime. Let a,b∈Z with p?a(a2+b2). In the paper we mainly determine by assuming p=c2+d2 or p=Ax2+2Bxy+Cy2 with AC−B2=a2+b2. As an application we obtain simple criteria for εD to be a quadratic residue , where D>1 is a squarefree integer such that D is a quadratic residue of p, εD is the fundamental unit of the quadratic field with negative norm. We also establish the congruences for and obtain a general criterion for p|U(p−1)/4, where {Un} is the Lucas sequence defined by U0=0, U1=1 and Un+1=bUn+k2Un−1(n?1). 相似文献
19.
We completely describe those positive Borel measures μ in the unit disc D such that the Bergman space Ap(w)⊂Lq(μ), 0<p,q<∞, where w belongs to a large class W of rapidly decreasing weights which includes the exponential weights , α>0, and some double exponential type weights.As an application of that result, we characterize the boundedness and the compactness of Tg:Ap(w)→Aq(w), 0<p,q<∞, w∈W, where Tg is the integration operator
20.
The numerical range W(A) of a bounded linear operator A on a Hilbert space is the collection of complex numbers of the form (Av,v) with v ranging over the unit vectors in the Hilbert space. In terms of the location of W(A), inclusion regions are obtained for W(Ak) for positive integers k, and also for negative integers k if A−1 exists. Related inequalities on the numerical radius and the Crawford number are deduced. 相似文献