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1.
Let X and Y be given Banach spaces. For AB(X), BB(Y) and CB(Y,X), let MC be the operator defined on XY by . In this paper we give conditions for continuity of τ at MC through continuity of τ at A and B, where τ can be equal to the spectrum or approximate point spectrum.  相似文献   

2.
When AB(H) and BB(K) are given, we denote by MC the operator acting on the Hilbert space HK of the form . In this note, it is shown that the following results in [Hai-Yan Zhang, Hong-Ke Du, Browder spectra of upper-triangular operator matrices, J. Math. Anal. Appl. 323 (2006) 700-707]
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3.
Daqing Yang 《Discrete Mathematics》2009,309(13):4614-4623
Let be a directed graph. A transitive fraternal augmentation of is a directed graph with the same vertex set, including all the arcs of and such that for any vertices x,y,z,
1.
if and then or (fraternity);
2.
if and then (transitivity).
In this paper, we explore some generalization of the transitive fraternal augmentations for directed graphs and its applications. In particular, we show that the 2-coloring number col2(G)≤O(1(G)0(G)2), where k(G) (k≥0) denotes the greatest reduced average density with depth k of a graph G; we give a constructive proof that k(G) bounds the distance (k+1)-coloring number colk+1(G) with a function f(k(G)). On the other hand, k(G)≤(col2k+1(G))2k+1. We also show that an inductive generalization of transitive fraternal augmentations can be used to study nonrepetitive colorings of graphs.  相似文献   

4.
Let B(H) denote the algebra of operators on an infinite dimensional complex Hilbert space H, and let AB(K) denote the Berberian extension of an operator AB(H). It is proved that the set theoretic function σ, the spectrum, is continuous on the set C(i)⊂B(Hi) of operators A for which σ(A)={0} implies A is nilpotent (possibly, the 0 operator) and at every non-zero λσp(A) for some operators X and B such that λσp(B) and σ(A)={λ}∪σ(B). If CS(m) denotes the set of upper triangular operator matrices , where AiiC(i) and Aii has SVEP for all 1?i?m, then σ is continuous on CS(m). It is observed that a considerably large number of the more commonly considered classes of Hilbert space operators constitute sets C(i) and have SVEP.  相似文献   

5.
The classical Weyl-von Neumann theorem states that for any self-adjoint operator A0 in a separable Hilbert space H there exists a (non-unique) Hilbert-Schmidt operator C=C? such that the perturbed operator A0+C has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering the set ExtA of self-adjoint extensions of a given densely defined symmetric operator A in H and some fixed . We show that the ac-parts and of and A0 are unitarily equivalent provided that the resolvent difference is compact and the Weyl function M(⋅) of the pair {A,A0} admits weak boundary limits M(t):=w-limy→+0M(t+iy) for a.e. tR. This result generalizes the classical Kato-Rosenblum theorem. Moreover, it demonstrates that for such pairs {A,A0} the Weyl-von Neumann theorem is in general not true in the class ExtA.  相似文献   

6.
Browder spectra for upper triangular operator matrices   总被引:1,自引:0,他引:1  
When AB(H) and BB(K) are given, we denote by MC the operator acting on the infinite dimensional separable Hilbert space HK of the form . In this paper, we prove that
  相似文献   

7.
When AB(H) and BB(K) are given, we denote by MC the operator matrix acting on the infinite-dimensional separable Hilbert space HK 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   

8.
Consider the generalized growth curve model subject to R(Xm)⊆?⊆R(X1), where Bi are the matrices of unknown regression coefficients, and E=(ε1,…,εs) and are independent and identically distributed with the same first four moments as a random vector normally distributed with mean zero and covariance matrix Σ. We derive the necessary and sufficient conditions under which the uniformly minimum variance nonnegative quadratic unbiased estimator (UMVNNQUE) of the parametric function with C≥0 exists. The necessary and sufficient conditions for a nonnegative quadratic unbiased estimator with of to be the UMVNNQUE are obtained as well.  相似文献   

9.
In this paper, we consider the stability to the global large solutions of 3-D incompressible Navier-Stokes equations in the anisotropic Sobolev spaces. In particular, we proved that for any , given a global large solution vC([0,∞);H0,s0(R3)∩L3(R3)) of (1.1) with and a divergence free vector satisfying for some sufficiently small constant depending on , v, and , (1.1) supplemented with initial data v(0)+w0 has a unique global solution in uC([0,∞);H0,s0(R3)) with ∇uL2(R+,H0,s0(R3)). Furthermore, uh is close enough to vh in C([0,∞);H0,s(R3)).  相似文献   

10.
We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], αR, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some KR, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all αR. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
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