The Characterization of a Class of Quantum Markov Semigroups and the Associated Operator-Valued Dirichlet Forms Based on Hilbert W＊-Module

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 l2 A and the set of regular quadratic forms, where A is a finite and a-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup （Tt）t∈R＋ C L（l2 A） is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L（l2 A） is the yon Neumann algebra of all adjointable module maps on l2 A.

STABILITY OF GENERALIZED DERIVATIONS ON HILBERT C*-MODULES ASSOCIATED WITH A PEXIDERIZED CAUCHY-JENSEN TYPE FUNCTIONAL EQUATION

In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.

A New Characterization on g-frames in Hilbert C^*-Modules

In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some properties of g-frames in Hilbert C;-modules（in Chinese）. Acta Math. Sinica, 2011, 54（1）: 1–8.).

CHAIN CONDITIONS FOR C＊-ALGEBRAS COMING FROM HILBERT C＊-MODULES

In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.

Pseudo Frame Decompositions in a Hilbert C＊-module H

In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C＊-module 74, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using .A-valued linear bounded operator U ： H → l^2（.A）, V＊U = I, a coustructing method of dual weak frame {xj^＊ ： j ∈ H} for a given weak frame {Xj ： j ∈ J} is obtained. Moreover, pseudo frame decompositions for 74 is given.

HILBERTW-模上标准广义框架的摄动

该文主要用算子理论的方法详细讨论了Hilbert W-模中标准广义框架的摄动性,且给出了类似于Hilbert空间中的很有用的摄动条件和相应结论.

Hilbert空间上算子W-加权Drazin逆的刻画及表示

该文研究了Hilbert空间上线性算子的W-加权Drazin逆,利用算子的分块矩阵表示,给出了W-加权Drazin逆的刻画及表示,所获结果推广了魏益民等的相关结果.

Hilbert W*-模上的广义框架(英文)

本文研究了Hilbert W*-模上的广义框架.运用了算子理论的方法,得出了Hilbert W*-模上的广义框架的一些结果,与标准离散Hilbert C*-模框架的一些结果是相似的.

C^(*)-Isomorphisms Associated with Two Projections on a Hilbert C^(*)-Module

Motivated by two norm equations used to characterize the Friedrichs angle,this paper studies C^(*)-isomorphisms associated with two projections by introducing the matched triple and the semi-harmonious pair of projections.A triple(P,Q,H)is said to be matched if is a Hilbert C^(*)-module,P and Q are projections on H such that their infimum P∧Q exists as an element of L(H),where L(H)denotes the set of all adjointable operators on H.The C^(*)-sub algebras of L(H)generated by elements in{P-P∧Q,Q-P∧Q,I}and{P,Q,P∧Q,I}are denoted by i(P,Q,H)and o(P,Q,H),respectively.It is proved that each faithful representation(π,X)of o(P,Q,H)can induce a faithful representation(π,X)of i(P,Q,H)such that π~(P−P∧Q)=π(P)−π(P)∧π(Q),π~(Q−P∧Q)=π(Q)−π(P)∧π(Q)..When(P,Q)is semi-harmonious,that is,R(P+Q) and R(2I−P−Q) are both orthogonally complemented in H,it is shown that i(P,Q,H)and i(I-Q,I-P,H)are unitarily equivalent via a unitary operator in L(H).A counterexample is constructed,which shows that the same may be not true when(P,Q)fails to be semi-harmonious.Likewise,a counterexample is constructed such that(P,Q)is semi-harmonious,whereas(P,I-Q)is not semi-harmonious.Some additional examples indicating new phenomena of adjointable operators acting on Hilbert C^(*)-modules are also provided.

The Sum of Standard Generalized Frames in Hilbert W^＊-Module

In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard generalized frames is a standard generalized frame.

The characterization of a class of quantum Markov semigroups and the associated operator-valued Dirichlet forms based on Hilbert C~*-module l_2(A)

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.

Takesaki-Takai Duality Theorem in Hilbert C^＊-Modules

In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).

Derivations on the Algebra of Operators in Hilbert C~*-Modules

Let M be a full Hilbert C＊-module over a C＊-algebra A, and let End^（.A4） be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End＊A（M） is an inner derivation, and that if A is a-unital and commutative, then innerness of derivations on ＂compact＂ operators completely decides innerness of derivations on EndA（M）. If .4 is unital （no commutativity is assumed） such that every derivation of A is inner, then it is proved that every derivation of EndA（Ln（A）） is also inner, where Ln（A） denotes the direct sum of n copies of A. In addition, in case A is unital, commutative and there exist xo,yo ∈M such that 〈xo,yo〉 = 1, we characterize the linear A-module homomorphisms on EndA（M） which behave like derivations when acting on zero products.

Compatibility and Schur Complements of Operators on Hilbert C~*-Module

Let E be a Hilbert C＊-module,and Y be an orthogonally complemented closed submodule of E.The authors generalize the definitions of Y-complementability and Y-compatibility for general（adjointable） operators from Hilbert space to Hilbert C＊-module,and discuss the relationship between each other.Several equivalent statements about Y-complementability and Y-compatibility,and several representations of Schur complements of Y-complementable operators（especially,of Y-compatible operators and of positive Y-compatible operators） on a Hilbert C＊-module are obtained.In addition,the quotient property for Schur complements of matrices is generalized to the quotient property for Schur complements of Y-complementable operators and Y＊-complementable operators on a Hilbert C＊-module.

基于镜像延拓和窗函数的端点效应抑制方法

经验模态分解被广泛用于复杂的非线性及非平稳信号处理,但其分解过程中存在端点效应问题,并且端点效应会随着筛选的进行而更加明显,从而导致数据处理发生畸变。镜像延拓法和窗函数法均是抑制端点效应的有效方法,但也各自存在不足。为此,提出将镜像延拓和余弦窗函数结合的改进方法,以弥补镜像延拓法中原始信号端点不是极值点和窗函数法中需要改变原信号的不足,实现对端点效应抑制方法的改进。仿真实验结果表明,与传统方法相比,改进方法能更好地抑制端点效应的发生。

Hilbert W~*-模上的广义框架(英文)

本文给出了Hilbert W＊-模上的标准广义框架的不相交,强不相交,弱不相交的定义,还给出了Hilbert W＊-模上的广义框架的不相交,强不相交,弱不相交成立的条件,并且用算子理论的方法研究了它们的性质.

一类Markov模算子半群与相应的算子值Dirichlet型刻画

本文基于Ⅱ_1-型因子把非交换对称Dirichlet型理论推广到算子值情形.在此框架下建立了算子值Dirichlet型,Markov模算子半群及Markov预解集之间的一一对应关系.

一类随机微分方程均方s渐进ω周期解的存在性（英文）

本文研究了在可分的实Hilbert空间中一类随机微分方程均方s渐进ω周期温和解的存在性问题.利用均方s渐进ω周期随机过程理论及Banach不动点定理,获得了此类方程均方s渐进ω周期温和解的存在及唯一性结果.最后给出相关例子来验证理论结果.

FREE FISHER INFORMATION AND AMALGAMATED FREENESS

The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness,i.e.,the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra.Cramer-Rao inequality in operator-valued settings is also obtained.

The Characterization of Certain Quantum Stochastic Stationary Process

In this paper we will obtain a Stone type theorem under the frame of Hilbert C＊-module, such that the classical Stone theorem is our special case. Then we use it as a main tool to obtain a spectrum decomposition theorem of certain stationary quantum stochastic process. In the end, we will give it an interpretation in statistical mechanics of multi-linear response.