Completion of operator partial matrices to square-zero contractions (Q1355224)

The authors study the square-zero completion and square-zero contraction completion for partial matrices of the form \[ {{A\;C}\choose {?\;?}}\qquad\text{and}\qquad {{A\;C}\choose {?\;B}}. \] They obtain necessary and sufficient conditions for such matrices to have square-zero completions and give a characterization of all such completions. As to the square-zero contraction completion, necessary and sufficient conditions are found for one type of matrices and some sufficient conditions for the other.