completely positive linear maps

作为从函数论到矩阵理论和算子论的推广，在积分、概率、张量积和非对易谱分析的许多方面都取得了丰硕的成果。 本文在前人研究成果的基础上，利用算子理论中的新方法，对完全正线性映射的数值值域和法向伸缩、凸结构、谱变分、矩阵综合、调和分析等问题进行了深入的研究。特别是，对量子信息的非对易方面的深入研究正在进行中。还将研究与两个等距/么正的泛C*-代数有关的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.