算子理论与算子代数中的Weyl-von Neumann定理在过去几十年里被广泛研究。近几年，由于在算子代数中引入了新的概念，Voiculescu定理（Voiculescu在1976年证明的非交换Weyl-von Neumann定理）已被部分推广为交换C*-代数（或AF代数）到半有限因子von Neumann代数的情形。本项目拟研究以下问题：（一）综合运用算子理论与算子代数的技巧，分析AF代数的C*-子代数的结构，以及研究它到半有限因子von Neumann代数的Voiculescu定理；（二）为了理解顺从C*-代数的结构，研究顺从C*-代数到有限因子von Neumann代数的“近似正交补”关系，以及它到半有限因子von Neumann代数的Voiculescu定理。. 对于以上问题的研究，将会进一步丰富和完善算子代数上Voiculescu定理的相关理论。

The Weyl-von Neumann theorem in operator theory and operator algebras has been extensively studied over the past several decades. In recent years, due to the introduction of new concepts in operator algebras, the Voiculescu's theorem (short for the Voiculescu's non-commutative Weyl-von Neumann theorem in 1976) for representations of unital commutative C*-algebras (or AF algebras) into semifinite von Neumann factors were proved. In this project, we will mainly study the following issues: (1) Combining the operator theory and operator algebras techniques, we will analyze the structure of the C*-subalgebras of AF algebras, and study the Voiculescu's theorem for representations of the C*-subalgebras of AF algebras into semifinite von Neumann factors; (2) In order to understand the structure of nuclear C*-algebras, we will study the approximate summands of representations of unital nuclear C*-algebras into finite von Neumann factors and the Voiculescu's theorem for representations of unital nuclear C*-algebras into semifinite von Neumann factors. . These investigations will further enrich and perfect the theory of the Voiculescu's theorem in operator algebras.