Invertibility And Invertible Completion Of Unbounded Operator Matrices

The research of operator matrices is very active in operator theory, and has important applications to pure and applied mathematics. The invertibility of unbounded singular∮-self-adjoint operator matrices is characterized, and a necessary and sufficient condition for certain partial operator matrices to exist invertible completion is further obtained. Moreover, some concrete examples are presented to illustrate our results.Also, the left invertibility of the unbounded upper triangular operator matrix is studied by the method of decomposing spaces, and a necessary and sufficient condition for a partial operator matrix to exist invertible completion is further obtained.