C~*-代数的实完全等距映射

C*-代数的*-同构一定是(完全)等距映射,反之不然.本文证明了C*-代数的实完全等距映射能够完全决定C*-代数*-同构的结论.     

C~* -代数上完全正映射的刻画

本文给出C* -代数之间完全正映射的刻画,证明:如果A,B是有单位元的C*-代数,则映射Φ:A→B为完全正映射当且仅当存在保单位*-同态πA:A→B(K)、等距* -同态πB:B→B(H)及有界线性算子V:H→K,使得πB(Φ(1))=V*V 且■a∈A,都有πB(Φ(a))=V*π(a)V.作为推论,得到著名的Stinespring膨胀定理.     

σ-C*-代数上的完全正映射和Stinespring型扩张定理

研究了σ-C*-代数上的完全正映射,获得了共变形式的Stinespring型扩张定理等一系列结果.所得结果推广和改进了某些已有的结果.     

关于连续迹C~*-代数间映射的谱

本文引进了连续迹C*-代数间映射的谱,并证明了其是C*-代数谱空间的 闭子集进而给出了刻划.同时,我们得到了诸如下半连续性等类似于形如C(X)Mn C*-代数间映射的谱性质.     

集值广义强向量拟均衡问题解的存在性

利用集值映射的自然拟C-凸性和集值映射的下(-C)-连续性的定义以及Kakutani-Fan-Glicksberg不动点定理,在不要求锥C的对偶锥C~*具有弱*紧基的情况下,建立了集值广义强向量拟均衡问题解的存在性定理.把相关文献中所得的关于单值映射解的存在性结果推广到了集值映射的情形.     

2×2矩阵代数上保持斜Lie积数值半径的映射（英文）

w(A)表示有界线性算子A的数值半径.本文完全刻画了2×2复矩阵代数M₂(C)上满足w(AB-BA^*)=w(Φ(A)Φ(B)-Φ(B)Φ(A)^*)对任意A,B∈M2(C)成立的一般映射Φ.     

Heisenberg和Schrdinger不确定关系中的不等式

本文通过C~*-代数上的保迹正线性映射,引入广义对称方差和广义对称相关系数的概念.证明了几个与Heisenberg和Schrdinger不确定关系相关的不等式,推广了已有的结论[J.Math.Phys.,2013,54(10):103508]和[J.Math.Anal.Appl.2017,447(1):666-680].     

广义强向量拟均衡问题组解的存在性

本文研究了一类集值广义强向量拟均衡问题组解的存在性问题.利用集值映射的自然拟C-凸性和集值映射的下(-C)-连续性的定义和Kakutani-Fan-Glicksberg不动点定理,在不要求锥C的对偶锥C~*具有弱*紧基的情况下,建立了该类集值广义强向量拟均衡问题组解的存在性定理.所得结果推广了该领域的相关结果.     

弱向量变分不等式的解集及其连通性

建立Hausdorff拓扑向量空间的非空凸子集到其值域为连续线性映射空间L(X, Y) 内的C -单调映射的弱向量变分不等式和它的纯量型变分不等式问题解的存在性, 讨论该弱向量变分不等式与之相联系的纯量型变分不等式解集的关系, 利用映射的C -弱次连续和C -单调性及其集值映射的不动点定理,通过纯量型变分不等式解集所诱导的集值映射所具有的特性给出弱向量变分不等式解集的连通性.     

关于fuzzy映射的完全广义混合强非线性变分包含

引入并研究了Hilbert空间中一类新的关于fuzzy映射的完全广义混合强非线性变分包含，利用极大单调映射的预解算子技巧构造迭代算法．并证明此变分包含的解的存在性及由迭代算法所生成的迭代序列的收敛性。所得结果改进并推广以往所得的相应结果。     

σ-C~-代数中的正映射

本文中我们研究了     

Covariant Projective Extensions

The theory of crossed products of C~*-algebras by groups of automorphisms is a well-developed area of the theory of operator algebras. Given the importance and the success ofthat theory, it is natural to attempt to extend it to a more general situation by, for example,developing a theory of crossed products of C~*-algebras by semigroups of automorphisms, or evenof endomorphisms. Indeed, in recent years a number of papers have appeared that are concernedwith such non-classical theories of covariance algebras, see, for instance [1-3].     

Stinespring representability and Kadison’s Schwarz inequality in non-unital Banach star algebras and applications

A completely positive operator valued linear map ϕ on a (not necessarily unital) Banach *-algebra with continuous involution admits minimal Stinespring dilation iff for some scalark > 0, ϕ(x)*ϕ(x) ≤ kϕ(x*x) for allx iff ϕ is hermitian and satisfies Kadison’s Schwarz inequality ϕ(h) ² ≤ kϕ(h ²) for all hermitianh iff ϕ extends as a completely positive map on the unitizationA _e of A. A similar result holds for positive linear maps. These provide operator state analogues of the corresponding well-known results for representable positive functionals. Further, they are used to discuss (a) automatic Stinespring representability in Banach *-algebras, (b) operator valued analogue of Bochner-Weil-Raikov integral representation theorem, (c) operator valued analogue of the classical Bochner theorem in locally compact abelian groupG, and (d) extendability of completely positive maps from *-subalgebras. Evans’ result on Stinespring respresentability in the presence of bounded approximate identity (BAI) is deduced. A number of examples of Banach *-algebras without BAI are discussed to illustrate above results.     

On Representations Associated with Completely n-Positive Linear Maps on Pro-C*-Algebras

It is shown that an n × n matrix of continuous linear maps from a pro-C*-algebra A to L(H), which verifies the condition of complete positivity, is of the formlinear operator from H to K, and [Tij]ni,j=1 is a positive element in the C*-algebra of all Suen in Proc. Amer. Math. Soc., 112(3), 1991, 709-712. Also, a covariant version of this construction is given.     

AF-algebras and topology of mapping tori

The paper studies applications of C*-algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2, 3 and 4. In conclusion, we consider two numerical examples illustrating our main results.     

The general Stone-Weierstrass problem and extremal completely positive maps

Let A be a C*-algebra with identity e and let B be a C*-subalgebra of A that contains e. We show that if B separates the pure states of A, then, for each n, B also separates the set ECP(A,ⁿ;I) of extremal completely positive unital maps of A into ⁿ, thus giving another equivalent condition for the general Stone-Weierstrass conjecture for C*-algebras.