MP Inverse And Weighted MP Inverse In Operator Algebras

This paper mainly studies some problems on Moore-Penrose inverse and the weighted Moore-Penrose inverse in C*-algebra. The thesis consists of four chapters:Chapter one introduces the background and problems of our studies, and lists some main results in the thesis.Chapter two introduces some definitions and theories of this paper. It introduces the Moore-Penrose inverse, ep element and coep element in Mn(C), C*-algebra and introduces the weighted Moore-Penrose inverse in Mn(C).Chapter three gives the conditions that the multiplication and addition of A(?), Aep are established; when.A is a type Ⅱ1factor, and extends some new and old results to the condition of M2(A).Chapter four deduces some results about weighted Moore-Penrose inverse of matrices by M-orthogonal projection and gives the theory of coep (M,N).