completely positive linear maps

作为从函数论到矩阵论和算子论的扩展，非对易谱分析在积分、概率、张量积等许多方面都取得了丰硕的成果。** 基于提出者以前的一些结果，本研究工作将通过算子理论中的新方法，在完全正线性映射的各种主题上进行，与数值范围和正常膨胀有关，与凸结构，谱变化，矩阵合成和调和分析有关。 特别是，量子信息的非对易性方面正在进行深入的研究。 也将研究与两个等距/酉的泛C*-代数相关的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.