completely positive linear maps

完全正线性映射

• 批准号: RGPIN-2014-03637
• 负责人: Choi, ManDuen
• 金额: $ 0.8万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=610558
• 关键词: completely; positive; linear; maps

As extensions from function theory to matrix theory and operator theory, there have been fruitful results on integrations, probability, tensor products and many aspects of non-commutative spectral analysis. Based on some previous results of the proposer, this research work will be carried out on a variety of topics on completely positive linear maps, in connection with numerical ranges and normal dilations, as related to convex structure, spectral variations, matrix synthesis, and harmonic analysis, by means of new approaches in operator theory. In particular, an intensive study is underwaybforn the non-commutative aspects of quantum information. There will also be an investigation on the crossed-products of C*-algebras related to the universal C*-algebras of two isometries/unitaries.

作为函数论到矩阵论和算子理论的延伸，在积分、概率、张量积以及非交换谱分析的许多方面都取得了丰硕的成果。 基于提议者之前的一些成果，这项研究工作将在完全正线性映射上的各种主题上进行，涉及数值范围和法向膨胀，如凸结构、谱变化、矩阵合成和谐波通过算子理论的新方法进行分析。特别是，针对量子信息的非交换方面的深入研究正在进行中。还将研究与两个等距/幺正的通用 C* 代数相关的 C* 代数的叉积。