Banach格的张量积的几何性质

本项目从建立任意两个Banach格正张量积的表示的创新方法出发，利用Banach格正张量积的表示来研究Banach格的Radon-Nikodym性质等各种重要性质在张量积是否还成立等问题。对Orlicz空间等具体空间的张量积的几何性质进行深入研究，提取分析出张量积可以继承的相关的几何性质，然后将讨论和研究这些几何性质在原子Banach格正张量积的继承性，并得到它们较好的刻画。建立一种全新的理论和方法来研究无限阶张量积的特征值和特征向量，进而研究Banach空间和Banach格无限阶张量积理论，得到Banach格无限阶张量积的全连续性质和Radon-Nikodym性质等的继承性刻画。此项工作将推进Banach空间和Banach格理论研究方法的变革，并推动Banach空间理论与Banach格的交叉领域和研究的深入发展。

This project starting from the establishment the representation of the positive tensor product of two Banach lattices, by using the representation of the positive tensor product of Banach lattices to study the inheritance of Radon-Nikodym property and other important properties in tensor product. The inheritance in tensor product of Orlicz spaces will be researched in depth, we can extract the geometric properties in the tensor product those can be inherited, and then discuss and study the inheritance of these geometric properties in the tensor product of atomic Banach lattices, and attain their characterization. Establish a new theory and methods to study the eigenvalues and eigenvectors, and study the infinite order tensor product of Banach spaces and Banach lattices, then attain the characterization of inheritance about the complete continuity property and the Radon-Nikodym property in the infinite order tensor product of Banach lattices. The work will promote the change of the research methods in Banach spaces and Banach lattices, and to promote the development of the intersection areas of Banach spaces and Banach lattices.