非交换Banach空间理论在量子统计物理、量子信息等领域有广泛应用. 本项目拟借助Banach空间几何理论与von Neumman代数理论为工具，研究Orlicz-Lorentz空间、赋Mazur-Orlicz拟范数Orlicz-Lorentz空间、定义在正规半有限忠实迹的半有限von Neumann代数的Orlicz-Lorentz空间、定义在Orlicz-Lorentz空间上的可测算子空间和可测算子对称空间的若干几何性质及其不动点性质. 给出Orlicz-Lorentz空间、非交换Orlicz-Lorentz空间、可测算子对称空间具有正规结构、一致非方和不动点性质的刻画，得到凸系数、弱光滑模等相应几何常数的计算程序. 建立赋Mazur-Orlicz拟范数Orlicz-Lorentz空间理论，讨论Mazur-Orlicz拟范数的单调性及空间的不动点性质.解决1-2个该方向的公开问题.

Theory of non-commutative Banach spaces is arises in a large number of applications in the fields of quantum statistical physics, quantum information. In this proposal, in virtue by theory of Banach spaces and theory of von Neumman algebra, normal structure, uniformly nonquare, fixed point property and some geometric coefficients as convex coefficent and modulus of weak smoothness will be discussed in Orlicz-Lorentz spaces, Orlicz-Lorentz spaces associated with an arbitrary semifinite von Neumann algebra with a faithful normal semifinite trace, symmetric spaces of measurable operators that the symmetric spaces is a Orlicz-Lorentz function spaces and symmetric spaces of measurable operators. This project is to define Orlicz-Lorentz spaces equipped with the Mazur-Orlicz norm, the relationships between modulus and norm will be given and the monotone of the Mazur-Orlicz norm and the fixed point property of Orlicz-Lorentz spaces equipped with the Mazur-Orlicz norm will be obtained. 1-2 open questions that are belong to my field will be solved.