An Introduction To C*-algebras And Finite-dimensional Approximations

This article mainly sorted out some basic definitions and theorems in C*-algebra and finite dimensional approximations[1],focus on finishing the Stinespring theorem,Arveson extension theorem and Voiculescu theorem.The article is based on the book of Brown and Ozawa[1] with some added detail of my understanding.Summarize these theorem can not only help me better study and understand the basic knowledge and content in the C*-algebra and finite dimensional approximations,but also lay a certain foundation for the future C*-algebra scholars,facilitating helping the people who want to know these theorems and basic knowledge to consult.Therefore,this article begins with some basic definitions and theorems which is the basis of the content of this article and the proof of later theorems.In this paper,the key is to introducting and proofing the Stinespring theorem,Arveson extension theorem and Voiculescu theorem detaily.It can help the readers better understand these theorems.In the proof of these theorems,there are a lot of methods can also be applied to other theorems’ proving.For example,in the proofing of Voiculescu theorem,the method of operator structure is worthy of reference and learning.At the same time,these theorems lay the foundation of learning approximation theory.