On the invertible completions of operator partial matrices
Huang Jian-ke · Journal of Northwest University · 2006
Aim To characterize the invertible assignment problem and the invertible completion on operator pairs. Methods Using the space decomposition, the polar decomposition and the construction technique in operator matrix. Results Given operators A and B acting on complex Hilbert spaces (?) and (?), respectively, the conditions indicate that there exists an operator F such that A + BF is invertible. Especially, for a partial operator matrix {A? B?} defined on (?), the sufficient conditions are gained to have a pair (X,Y) of operators such that MX,Y = (AX BY) is invertible. Conclusion By using the results obtained, the invertible completion can be further explored.