| C~* -代数上完全正映射的刻画 |
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| 引用本文： | 银俊成,曹怀信. C~* -代数上完全正映射的刻画[J]. 应用数学, 2012, 25(2): 357-362 |
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| 作者姓名： | 银俊成 曹怀信 |
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| 作者单位： | 1. 陕西师范大学数学与信息科学学院,陕西西安710062;中国计量学院理学院,浙江杭州 310018
2. 陕西师范大学数学与信息科学学院,陕西西安,710062 |
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| 基金项目： | 国家自然科学基金资助项目，陕西省科技计划项目 |
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| 摘 要： | 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.
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| 关 键 词： | 完全正映射 Stinespring膨胀定理 C*-代数 表示 |
The Characterization of Completely Positive Mappings on C* -algebra |
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| YIN Juncheng , CAO Huaixin. The Characterization of Completely Positive Mappings on C* -algebra[J]. Mathematica Applicata, 2012, 25(2): 357-362 |
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| Authors: | YIN Juncheng CAO Huaixin |
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| Affiliation: | 1(1.College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China;2.College of Science,China Jiliang University,Hangzhou 310018,China) |
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| Abstract: | In this paper,we give the characterization of completely positive mappings on C*-algebra.It is proved that if A and B are C*-algebras with identity,Φ:A→B is a completely positive mapping if and only if there are a unit-preserving *-homomorphism πA:A→B(K),an isometric *-homomorphism πB:B→B(H) and a bounded linear operator V:H→K such that πB(Φ(1))=V*V and πB(Φ(a))=V*πA(a)V,■a∈A.Meanwhile,we get the famous Stinespring’s dilation theorem as a corollary. |
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| Keywords: | Completely positive map Stinespring’s dilation theorem C*-algebra Representation |
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