共查询到20条相似文献,搜索用时 140 毫秒
1.
本文证明,如果Hilbert空间上交换自伴算子组T=(T1,…,Tn)的Taylor谱之Hausdorff直维数等于α,α≥1,则对任意的p>α,存在Cp-范数充分小的Cp-类算子组K,使得T-K是交换对角算子组。 相似文献
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加权Dirichlet空间上的复合算子 总被引:4,自引:0,他引:4
本文研究复平面中单位圆盘的加权Dirichlet空间上的复合算子Cψ。利用Carleson测度的概念,给出了Cp为有界算子,紧算子的充要条件。同时,对复合算子Cp为Schatten P-类算子时,函数ψ应满足的条件作了讨论,给出了积分形式的刻划。 相似文献
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拟相似算子的右本质谱的连通分支 总被引:1,自引:0,他引:1
设算子S和T拟相似,通过引进RT类算子、R类算子和RR类算子的概念,给出右本质谱σre(S)的连通分支与σre(T)相交的充分条件和必要条件以及σre(S)的连通分支与本质谱盯σe(T)的某些子集的相交关系,并给出算子是属于RT类算子和RR类算子的充分条件和必要条件. 相似文献
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给定Hilbert空间L2[a,∞)上两个由2n阶对称微分算式生成的微分算子Li(i=1,2),该文给出了乘积算子L2L1是自伴算子的一个充分必要条件. 相似文献
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王红军赵佳 《应用泛函分析学报》2020,(4):207-218
本文研究了度量图上二阶及四阶局部微分算子积的自伴顶点条件.在研究闭区间[a,b]上积算子自伴性的基础上,运用度量图上高阶局部微分算子的自伴顶点条件得到了积算子自伴的充分必要条件.此外,给出了积算子自伴与原算子自伴之间的关系. 相似文献
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利用算子理论及矩阵运算方法,讨论了由两类不同的对称微分算式D~((4))+D~((2))+q_1(t)和D~((4))+q_2(t)(D=d/dt,t∈I=[a,b])生成的微分算子的积算子的自伴性,获得了积算子是自伴算子的充分必要条件. 相似文献
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利用矩阵运算及算子的基本理论,讨论了由微分算式L_1=D~((2))+q_1(t)和L_2=D~((4))+q_2(t)其中(D=d/dx,t∈I=[a,b])生成的两个微分算子L_i(i=1,2)积L_1L_2的自伴性问题,并在常型情形下,获得了积算子自伴的充分必要条件. 相似文献
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首先利用算子比较的方法,研究了二项自伴向量微分算子的本质谱,得到了这类微分算子的本质谱分布范围;然后利用算子分解定理,得到了这类算子谱的离散性的一个充分条件;最后得到了Sturm-Liouville算子和Schr?dinger算子的本质谱范围,以及这两类算子谱的离散性的一个充分条件. 相似文献
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This paper investigates the asymptotic decay of the singular values of compact operators arising from the Weyl correspondence. The motivating problem is to find sufficient conditions on a symbol which ensure that the corresponding operator has singular values with a prescribed rate of decay. The problem is approached by using a Gabor frame expansion of the symbol to construct an approximating finite rank operator. This establishes a variety of sufficient conditions for the associated operator to be in a particular Schatten class. In particular, an improvement of a sufficient condition of Daubechies for an operator to be trace-class is obtained. In addition, a new development and improvement of the Calderón–Vaillancourt theorem in the context of the Weyl correspondence is given. Additional results of this type are then obtained by interpolation. 相似文献
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Given a bounded selfadjoint operator a in a Hilbert space , the aim of this paper is to study the orbit of a, i.e., the set of operators which are congruent to a. We establish some necessary and sufficient conditions for an operator to be in the orbit of a. Also, the orbit of a selfadjoint operator with closed range is provided with a structure of differential manifold.
相似文献
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Siberian Mathematical Journal - We establish sufficient conditions for the zero to belong to the limit spectra of some unbounded selfadjoint integral operator. 相似文献
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设X为无限维可分的Banach空间,T是X上的有界线性算子.利用轨道C·Orb(x,T)的d稠密性给出了T是亚超循环算子的充分条件.此外,还考虑可逆的亚超循环算子T并从循环向量的角度刻画了T和T~(-1)的亚超循环性. 相似文献
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孙志玲 《数学物理学报(A辑)》2020,(2):304-314
该文给出了多圆盘Bergman空间上两个带有某种符号的Toeplitz算子的乘积等于另一个Toeplitz算子的充分必要条件,并且给出了乘积算子所带符号的公式.接下来,相应的研究了它的交换性.这些研究结果都是根据符号函数的Mellin变换. 相似文献
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This is a sequel of the article by Borichev, Golinskii and Kupin (2009) [1], where the authors obtain Blaschke-type conditions for special classes of analytic functions in the unit disk, which satisfy certain growth hypotheses. These results were applied to get Lieb–Thirring inequalities for complex compact perturbations of a selfadjoint operator with a simply connected resolvent set. The first result of the present paper is an appropriate local version of the Blaschke-type condition from Borichev et al. (2009) [1]. We apply it to obtain a similar condition for an analytic function in a finitely connected domain of a special type. Such condition is by and large the same as a Lieb–Thirring type inequality for complex compact perturbations of a selfadjoint operator with a finite-band spectrum. A particular case of this result is the Lieb–Thirring inequality for a selfadjoint perturbation of the Schatten class of a periodic (or finite-band) Jacobi matrix. 相似文献
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詹牡君 《数学的实践与认识》2012,42(24)
讨论了B~α空间和Q_K空间之间的加权Cesro算子T_g的有界性,给出了B~α空间到Q_K空间的加权Cesro算子T_g有界的充要条件.另外也给出了Q_K空间到B~α空间的加权Cesro算子T_g有界的充要条件. 相似文献
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Let S be the multiplication operator by an independent variable x in L
2(0,1), and let V be an integral operator of Volterra type. In this note, we find sufficient conditions for the similarity of the operators T := S + V and S and discuss some generalizations to an abstract setting of the results obtained. 相似文献
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本文研究单位圆盘上的BMOA空间和$\a$-Bloch型空间之间的加权 Ces\'{a}ro 算子,给出了$\tg$是BMOA空间到$\ba$空间的有界算子或紧算子的充分必要条件. 相似文献
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On the harmonic Bergman space of the half-space, we give characterizations for an arbitrary positive Toeplitz operator to
be a Schatten (or Schatten-Herz) class operator in terms of averaging functions and Berezin transforms. Examples are provided
to show that various results are sharp.
This research was supported by KOSEF(R01-2003-000-10243-0). 相似文献