| Kadison-Singer代数研究综述 |
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| 引用本文： | 董瑷菊,陈广锋,杨渭清,张运良,安军龙.Kadison-Singer代数研究综述[J].数学学报,2018,61(2):177-196. |
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| 作者姓名： | 董瑷菊 陈广锋 杨渭清 张运良 安军龙 |
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| 作者单位： | 西安文理学院信息工程学院数学系 西安 710065 |
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| 基金项目： | 国家自然科学基金资助项目（11371290）；陕西自然科学基础研究计划项目（2017JM1045） |
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| 摘 要： | 回顾了建立KS-代数的研究背景,系统介绍了KS-代数的定义和性质以及超有限KS-代数、非超有限KS-代数、KS-格的构造和强KS-代数的研究结果,同时分析了KS-代数和经典的不变子空间、Kadison可迁代数、von Neumann代数生成元等问题之间的联系;讨论了非自伴代数的运算,给出了两种不同构造非自伴代数的运算法则;在此基础上,提出了未来学科发展有待研究的16个问题.
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| 关 键 词： | 自反代数 自反子空间格 von Neumann代数 KS-代数 强KS-代数 |
Survey on Kadison-Singer Algebras |
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| Ai Ju DONG,Guang Feng CHEN,Wei Qing YANG,Yun Liang ZHANG,Jun Long AN.Survey on Kadison-Singer Algebras[J].Acta Mathematica Sinica,2018,61(2):177-196. |
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| Authors: | Ai Ju DONG Guang Feng CHEN Wei Qing YANG Yun Liang ZHANG Jun Long AN |
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| Affiliation: | Department of Mathematics, School of Information Technology, Xi'an University, Xi'an 710065, P. R. China |
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| Abstract: | The background for the introduction of Kadison-Singer algebras (KSalgebras, for short) is reviewed. Definitions and basics properties are explained. Studies on hyperfinite KS-algebras, non-hyperfinite case, KS-lattices and strong KS-algebras are described in details, as well as their connections with classical open problems such as the invariant subspace problem, Kadison's transitive algebra problem, von Neumann algebra generator problem. Operations on non-selfadjoint operator algebras are also discussed and two new operations are included in the discussion. Sixteen open problems are listed with some explanations in the end. |
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| Keywords: | reflexive algebras reflexive lattices von Neumann algebras KS-algebras strong KS-algberas |
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