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A Bishop-Stone-Weierstrass Theorem for (M_2(C))~n

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Acta Mathematica Sinica,English Series 2013年第8期29卷 1515-1534页

作者： Qi Hui LI don hadwin Department of Mathematics East China University of Science and Technology Department of Mathematics and Statistics University of New Hampshire

In this paper, we shall give an elementary proof of a Bishop–Stone–Weierstrass theorem for （M2（C））n with respect to its pure states. To be more precise, we shall show that the pure-state Bishop hull of a unital ... 详细信息

关键词： Bishop–Stone–Weierstrass theorem pure states C*-algebras

A modified version of free orbit-dimension of von Neumann algebras

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Science China Mathematics 2011年第11期54卷 2329-2346页

作者： hadwin don LI WeiHua Mathematics Department University of New Hampshire Durham NH 03824 USA Science and Mathematics Department Columbia College Chicago Chicago IL 60605 USA

Based on the notion of free orbit-dimension of hadwin-Shen (2007) we introduce a new invariant for finite von Neumann algebras with arbitrarily large generating sets and acting on Hilbert spaces of arbitrary dimension. We show that this invariant is independent of the generating set, and we extend results in hadwin-Shen (2007) to this larger class of algebras.

关键词： von Neumann algebras free entropy dimension free orbit dimension

Universal C*-algebras Defined by Completely Bounded Unital Homomorphisms

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Acta Mathematica Sinica,English Series 2015年第12期31卷 1825-1844页

作者： Wen Hua QIAN don hadwin Department of Mathematics East China University of Science and Technology Department of Mathematics and Statistics University of New Hampshire

Suppose A is a unital C＊-algebra and r *** this paper,we define a unital C＊-algebra C（cb）＊（A,r） and a completely bounded unital homomorphism αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C＊（αr（A））and,for every unital C＊-algebra B and every unital completely bounded homomorphism φ：A→ B,there is a（unique）unital ＊-homomorphism π：C（cb）＊（A,r）→B such thatφ=πoα*** prove that,if A is generated by a normal set {tλ：λ∈Λ},then C（cb）＊（A,r）is generated by the set {αr（tλ）：λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C（cb）＊（A,r）we obtain that,if Β is a unital C＊-algebra that can be embedded into A,then C（cb）＊（B,r）can be naturally embedded into C（cb）＊（A,r）.We give characterizations of C（cb）＊（A,r）for some special situations and we conclude that C（cb）＊（A,r）will be ＂nice＂ when dim（A）≤ 2 and ＂quite complicated＂ when dim（A）≥ *** give a characterization of the relation between K-groups of A and K-groups of C（cb）＊（A,r）.We also define and study some analogous of C（cb）＊（A,r）.

关键词： Completely bounded unital homomorphisms universal C*-algebras K-groups

Injectivity and projectivity in analysis and topology

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Science China Mathematics 2011年第11期54卷 2347-2359页

作者： hadwin don PAULSEN Vern I Department of Mathematics University of New Hampshire Durham NH 03824 USA Department of Mathematics University of Houston Houston TX 77204-3008 USA

We give new proofs of many injectivity results in analysis that make more careful use of the duality between abelian C*-algebras and topological spaces. We then extend many of these ideas to incorporate the case of a group action. This approach gives new insight into Hamana's theory of G-injective operator spaces and G-injective envelopes. Our new proofs of these classic results, use only topological methods and eliminate the need for results from the theory of Boolean algebras and AW*-algebras.

关键词： injective multipliers operator space Banach-Stone

具有无限重数的算子到正规算子集的距离估计与不可分的BDF定理

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中国科学：数学 2016年第2期46卷 123-128页

作者：张邺 hadwin don 陈艳妮陕西师范大学数学与信息科学学院西安710119 Department of Mathematics and Statistics University of New Hampshire

设T为Hilbert空间H上的有界线性算子,T^((n))表示n个T的直和,其中n=1,2,...,∞.本文给出了T^((∞))到全体正规算子的距离估计,并指出T^((n))到正规算子集的距离会因n是否为∞而引起大幅的变化.借助于该距离估计,本文证明了,若H为不可分H... 详细信息

设T为Hilbert空间H上的有界线性算子,T^((n))表示n个T的直和,其中n=1,2,...,∞.本文给出了T^((∞))到全体正规算子的距离估计,并指出T^((n))到正规算子集的距离会因n是否为∞而引起大幅的变化.借助于该距离估计,本文证明了,若H为不可分Hilbert空间,K为B(H)的非紧算子理想,则B(H)/K中的正规算子都可表示为B(H)中的一个正规算子与K中的一个算子之和.

关键词：不可分Hilbert空间 Calkin代数正规算子基数紧算子