completely positive linear maps

作为函数理论向矩阵理论和算符理论的扩展，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。本文将在前人研究成果的基础上，利用算子理论的新方法，对完全正线性映射、数值范围和正态膨胀、凸结构、谱变化、矩阵合成和谐波分析等问题进行研究。特别是，对量子信息的非交换方面的深入研究正在进行中。本文还将研究C*-代数与两个等距单位的普适C*-代数的交叉积。

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.