Author: Yisheng Huang
Language: English
ISBN/ISSN: 7030222268
2009; Hardcover; 228
We now briefly outline the contents of the book. Chapter 1 is devoted to basic results of metric spaces, especially an important fixed point theorem called the Banach contraction mapping theorem, and its applications. Chapter 2 deals with basic definitions, properties and examples related to the normed linear space, especially, Banach spaces. The beautiful theory of inner product space, especially Hilbert spaces, which draws connections between the first two chapters, is introduced and discussed in detail in Chapter 3. In Chapter 4, we describe general properties of linear operators between normed linear spaces, in addition, important results such as the uniform bounded principle, open mapping and closed graph theorems, the Banach theorem, the Hahn-Banach theorem, the representation theorems for some dual spaces and the concept of weak convergence are presented. Chapter 5 is devoted the nice properties of a class of linear operators, compact and self-adjoint operators, acting between Hilbert spaces and their spectral properties.
Language: English
ISBN/ISSN: 7030222268
2009; Hardcover; 228
We now briefly outline the contents of the book. Chapter 1 is devoted to basic results of metric spaces, especially an important fixed point theorem called the Banach contraction mapping theorem, and its applications. Chapter 2 deals with basic definitions, properties and examples related to the normed linear space, especially, Banach spaces. The beautiful theory of inner product space, especially Hilbert spaces, which draws connections between the first two chapters, is introduced and discussed in detail in Chapter 3. In Chapter 4, we describe general properties of linear operators between normed linear spaces, in addition, important results such as the uniform bounded principle, open mapping and closed graph theorems, the Banach theorem, the Hahn-Banach theorem, the representation theorems for some dual spaces and the concept of weak convergence are presented. Chapter 5 is devoted the nice properties of a class of linear operators, compact and self-adjoint operators, acting between Hilbert spaces and their spectral properties.
You May Also Like
