共查询到19条相似文献,搜索用时 46 毫秒
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本文研究了带有Radon-Nikodym导数的算子值自由Fisher信息量.利用模框架理论,得到了一个半圆元和一个子代数之间的合并自由关系,推广了D.Voiculescu等人的工作. 相似文献
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在Hilbert C*-模框架下建立了Co-模半群,获得了量子Stone型定理,以此为工具给出了一类量子随机过程的谱分解. 相似文献
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观察到Hilbert C*-模中融合框架原定义的不合理性,然后通过权重集的选取将其改进,得到融合框架的新定义并给出其等价形式.特别地,利用算子理论方法得到了Hilbert C*-模中融合框架的一个新刻画. 相似文献
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本文运用算子理论方法,给出Hilbert C~*-模中g-框架的一些性质并讨论g-框架的扰动性,得到g-框架的和的一些刻画,所得结果推广和改进了已有的结果. 相似文献
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本文引入了Hilbert C*-模上的Gabor酉系统的概念,研究了它的基本性质,证明了膨胀定理,并给出某个酉系统的两个正规框架向量不相交的等价条件. 相似文献
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本文引入了有界广义逆模映射的概念,并给出了等价刻画.然后利用它为工具获得了一类重要的有界模映射的因子分解定理,使得著名的Douglas分解定理成为其特例. 相似文献
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本文研究Hilbert C*-模中K-框架的不等式问题.借助K-对偶构建了闲子模中K-框架的几个新的不等式,所得结果推广和改进了Hilbert空间中框架和Hilbert C*-模中广义框架的相应结果. 相似文献
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Bin Meng Maozheng Guo Xiaohong Cao 《Proceedings of the American Mathematical Society》2005,133(10):3087-3096
We introduce the operator-valued free Fisher information for a random variable in an operator-valued noncommutative probability space and point out its relations to the amalgamated freeness. Using M. Frank and D. Larson's modular frame notion we can construct the conjugate variable for an operator-valued semicircle variable with conditional expectation covariance. Then we obtain its free Fisher information and show it is equal to the index of the conditional expectation. At last the conjugate variable with respect to a modular frame operator for a semicircle variable is also constructed.
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In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W*-module l2 A, and give a one to one correspondence between the set of positive self-adjoint regular module operators on l2A and the set of regular quadratic forms, where A is a finite and σ-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup {Tt }t∈R + L(l2A) is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L(l2A) is the von Neumann algebra of all adjointable module maps on l2A. 相似文献
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We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form. 相似文献
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设 E是 Hilbert C~*-模,证明了E的每个闭子模均可补的充要条件是 K(E)的每个非零遗传C~*-子代数B,均有形式B=pK(E)p,其中p为L(E)中投影元。 相似文献
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在Hilbert C~*-模框架下,给出了闭子模之间的酉等价与相应的遗传C~*-子代数的*同构,及对应的开投影的等价性的关系定理. 相似文献
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给出了算子值半圆分布的各阶公式.引入算子值随机变量之间一种新的关系-半独立,并在此意义下给出算子值半圆分布的随机矩阵模型.最后证明了若干个半独立的半圆元的矩阵模型是渐进自由的. 相似文献
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孟彬 《数学物理学报(B辑英文版)》2010,30(4):1327-1337
The free Fisher information of an operator random matrix is studied. When the covariance of a random matrix is a conditional expectation, the free Fisher information of such a matrix is the double of this conditional expectation’s Watatani index. 相似文献
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设 G=(A,△)为紧矩阵量子群,G为A的所有有限维光滑的、不可约余表示等价类的集合.本文通过(A,△)的一个余表示Vo构造了两个相互配对的集合,利用Hilbert C*-模的理论证明它们分别为A和Baaj与Skandalis构造的量子群A,并且证明了对任意的α∈G,在A中都对应一个有限维投影算子Pα,满足 dim(α)=dim(pα). 相似文献