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1.
本文讨论了酉算子的散射和符号算子问题。证明的主要结果如下:(1)如果U,V为Hilbert空间H上酉算子,J为有界线性算子,使UJ-JV是迹类算子,那么存在。(2)若U为绝对连续的酉算子,T为有界线性算子,使是迹类算子,那么存在。  相似文献   

2.
该文在算子值非交换概率空间上引入半标准酉随机矩阵的概念, 证明了它是算子值Haar酉元的矩阵模型,并给出了半标准酉随机矩阵的渐近自由判定定理.  相似文献   

3.
本文证明了Π_k空间上强连续的压缩算子半群均具有酉扩张,还讨论了压缩算子半群的协生成元和扩张酉半群之间的关系,并且精确估计了Π_k上强连续J-酉算子半群的增长阶。  相似文献   

4.
研究Hilbert空间上有界线性算子的(ω)性质,给出了广义Kato型的定义并根据广义Kato型的性质定义了一种新的谱集,利用该谱集给出了Hilbert空间上有界线性算子满足(ω)性质的充要条件,并且讨论了(ω)性质的稳定性.  相似文献   

5.
罗群 《数学研究》1995,28(2):76-82
本文给出复随机内积模上几乎处处有界线性算子谱的几个基本定理,这些定理不但为随机内积模上几乎处处有界线性算子的进一步讨论有基本重要性,而且也为Hilbert空间上连续随机算子的谱研究提供了一个新途径。  相似文献   

6.
给出复可分Hilbert空间上任意重的算子权移位是紧算子的充要条件,重新证明了每个算子权移位酉等价于一个正算子权移位并讨论了算子权移位S~{Wk}与T~{|Wk|}的关系,给出了压缩的任意重算子权移位的Cαβ分类的充要条件.  相似文献   

7.
K-框架是框架理论的一种推广.K-框架可以用于重构Hilbert空间中有界线性算子值域内的元素.本文首先研究了K-框架与框架理论的关系,得到了紧K-框架成为框架当且仅当有界线性算子K是满的,给出了有界线性算子K具有闭值域的K-框架的一个充要条件.并利用有界线性算子K和合成算子构造K-框架,讨论在一定扰动条件下K-框架的稳定性.  相似文献   

8.
若B(H)表示希尔伯特空间H中所有有界线性算子之集.本文研究了定义在B(H)上的初等算子和广义导算子的范数可达性,证明了如果定义在B(H)中的初等算子和广义导算子是范数可达的,那么这些算子在B(H)中酉群上的限制也是范数可达的.  相似文献   

9.
对于Π_1空间上J-正常算子的J-酉等价问题进行讨论.针对不同情况,给出了Π_1空间上两个J-正常算子J-酉等价的充要条件.这将有助于研究Π_1空间上交换J-von Neumann代数之间的J-酉等价.  相似文献   

10.
Ba空间中Kantorovich算子的饱和性   总被引:16,自引:0,他引:16  
盛保怀 《数学杂志》1992,12(2):146-154
本文给出了 B_a 空间的对偶空间,初步讨论了 B_a 空间中,Hardy-Littlewood 极大函数及 B_a 空间中有界线性泛函的性质,进而讨论了B_a空间中 Kantorovich 算子的饱和性。  相似文献   

11.
Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, the authors explore a pure algebraic version of the dilation theory for linear systems acting on unital algebras and vector spaces. By introducing two natural dilation structures, namely the canonical and the universal dilation systems, they prove that every linearly minimal dilation is equivalent to a reduced homomorphism dilation of the universal dilation, and all the linearly minimal homomorphism dilations can be classified by the associated reduced subspaces contained in the kernel of synthesis operator for the universal dilation.  相似文献   

12.
The dilations for operator-valued measures (OVMs) and bounded linear maps indicate that the dilation theory is in general heavily dependent on the Banach space nature of the dilation spaces. This naturally led to many questions concerning special type of dilations. In particular it is not known whether ultraweakly continuous (normal) maps can be dilated to ultraweakly continuous homomorphisms. We answer this question affirmatively for the case when the domain algebra is an abelian von Neumann algebra. It is well known that completely bounded Hilbert space operator valued measures correspond to the existence of orthogonal projection-valued dilations in the sense of Naimark and Stinespring, and OVMs with bounded total variations are completely bounded but not the vice-versa. With the aim of classifying OVMs from the dilation point of view, we introduce the concept of total p-variations for OVMs. We prove that any completely bounded OVM has finite 2-variation, and any OVM with finite p-variation can be dilated to a (but usually non-Hilbertian) projection-valued measure of the same type. With the help of framing induced OVMs, we prove that conventional minimal dilation space of a non-trivial framing contains c0, then does not have bounded p-variation.  相似文献   

13.
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a Banach space. This completely generalizes a well-known result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group. We also prove that isometric group representation induced framings on a Banach space can be dilated to unconditional bases with the same structure for a larger Banach space. This extends several known results on the dilations of frames induced by unitary group representations on Hilbert spaces.  相似文献   

14.
We study the problem of determining which bounded linear operator on a Hilbert space can be dilated to a singular unitary operator. Some of the partial results we obtained are (1) every strict contraction has a diagonal unitary dilation, (2) everyC 0 contraction has a singular unitary dilation, and (3) a contraction with one of its defect indices finite has a singular unitary dilation if and only if it is the direct sum of a singular unitary operator and aC 0(N) contraction. Such results display a scenario which is in marked contrast to that of the classical case where we have the absolute continuity of the minimal unitary power dilation of any completely nonunitary contraction.  相似文献   

15.
A new function model for an arbitrary bounded operator on a Hilbert space is constructed. This model generalizes the model of Sz.-Nagy and Foiaş for contractions and seems to be useful for operators close to an isometry (in a sense). All the model spaces are Hilbert spaces, but instead of dilation a generalization of it is used. The model admits a symmetry with respect to the map z→1/z of the complex plane. In terms of the model the question of lifting the commutant is investigated, a relationship between invariant subspaces of a unitary operator is established, and the characteristic function of the model operator is calculated. Some other problems are solved as well. Bibliography: 8 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 201, 1992, pp. 95–116. Translated by V. Vasyunin.  相似文献   

16.
In this paper, the author considers the generalized dilations of operator sequences in a Hilbert space to a Krein space. In order to obtain the unitary and solf-adjoint dilations, only some boundedness and symmetry assumptions are needed.  相似文献   

17.
A model for non-contractive functions is given, according to which every bounded analytic function coincides with the characteristic function of a suitable unitary colligation. In our construction, the function is expressed in terms of a fundamentally reducible unitary dilation of the basic operator of the colligation.The results in this paper first appeared as part of the author's doctoral thesis [13] at the Universidad Central de Venezuela, under the supervision of Mischa Cotlar. The work has been supported by the Consejo Nacional de Investigaciones Cientificas y Techológicas (CONICIT-Venezuela). I am grateful to Professor Aad Dijksma, who read an earlier version of this note and made several helpful criticisms. I also thank Professor Mischa Cotlar for his kind encouragement and Professor Alejandra Cabana for correcting the english text.  相似文献   

18.
Two types of estimate for the spectral radius of the multivariate refinement operator with power diagonal dilations are presented. One type contains multiplicator norm of number matrices generated by the symbol of the corresponding operator and by specific subsets of repeating fractions. These subsets are used together with the little Fermat theorem to establish estimates that comprise integrals over tori of various dimensions. Moreover, we note certain classes of symbols when the exact value of the spectral radius of refinement operator can be found. For the spectral radius of subdivision operators point value estimates are established. Submitted: April 25, 2007. Accepted: November 5, 2007.  相似文献   

19.
本文用奇异值刻划了具有指定阶酉扩张的矩阵类,同时讨论了矩阵的正规扩张问题  相似文献   

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