The Pseudo-inverse Operators Of Linear Operators In Hilbert Space And Its Applications

Pseudo-inverse operator was first introduced by Fredholm in 1902,the notion of the pseudo-inverse is a concept frequently used in operator theory which has some practical concrete applications,see[8],[9].An important application of pseudo-inverse operators are in the frame theory.In this paper,we mainly study the pseudo-inverse of linear operators and its properties,applications.In chapter 1,we will make a general description on the researches in our field and show the main results of this paper.In chapter 2,we introduce the preliminaries for the paper.In chapter 3,we establish the pseudo-inverse of linear bounded operator with closed range,and prove its properties,at last,we will give an example from which we can see the use of pseudo-inverse in frame theory.In chapter 4,we establish the pseudo-inverse of linear bounded operator,the range of which is not closed.In chapter 5,we discuss the pseudo-inverse of linear unbounded closed operator ,the range of which is closed,and give the use of it.