本项目拟研究的内容是与非交换函数空间理论和非交换调和分析相关联的一些问题。它们是非交换分析理论的有机组成部分，也是当前泛函分析领域中的一个比较活跃的研究方向。首先我们将借助人们研究非交换对称空间和非交换Lp空间的方法来研究非交换Calderon-Lozanovskii空间和加权非交换Lp空间上的乘积空间、对偶空间、插值空间、乘子空间等问题。然后再结合非交换Hardy空间理论中的方法来研究非交Calderon-Lozanovskii-Hardy空间和加权非交换Hardy空间上的一系列问题，包括Riesz和Szego型分解定理、插值空间、对偶空间、内-外分解和外算子的性质、次对角代数的分解性质、Beurling型不变子空间定理、Nehari-Type定理等问题。我们将先在有限von Neumann代数的情形下讨论上述问题，然后再推广到半有限的情形上去。

In the project, some problems related to the theory of noncommutative harmonic analysis and noncommutative function spaces is considered. As an essential part of the theory of noncommutative analysis, they are also an active research orientat- ion in the field of functional analysis.At first, interpolation spaces, space of multipliers, dual spaces, as well as product spaces of noncommutative Calderon- Lozanovskii spaces and weighed noncommutative Lp spaces are considered by using some method developed in the research on noncommutative symmetric spaces theory and noncommutative Lp space. Then, a series of problems in noncommutative Calderon -Lozanovskii-Hardy spaces and weighted noncommutative Hardy spaces are studied by means of the theory of noncommutative Hardy spaces, including Szego and Riesz type factorization theorem, interpolation spaces, dual spaces,factorization properties of subdiagonal algebras, inner-outer type factorizations and characterization of outer elements, Beurling theorem, Nehari-Type theorem, etc.The above problems will be firstly considered when von Neumann algebra is finite, thus we will extend it to the case of semifinite.