Bott-Duffin Inverse Of Linear Relations

The generalized inverse of linear relations has a very important role in relation theory and concrete applications.The existence and the matrix representation of the Bott-Duffin inverse of bounded operators on Hilbert spaces have been obtained,but the corresponding results have not been reported for linear relations.In this thesis,we first introduce the Bott-Duffin inverse of linear relations on Banach spaces,and the relationship among the linear relation A,the projection operator PM,N and the Bott-Duffin inverse AM,N-1 is discussed.Some necessary and sufficient conditions are given for a linear relation to be Bott-Duffin invertible,and the matrix representation of Bott-Duffin inverse AM,N-1 is further provided.