中文摘要：

基于右上角元素值域的闭性和某空间族的维数扰动，得到了缺项四分块算子矩阵（A？CD）存在Fredholm补的一个新的充分必要条件，结果表明该类补问题可以转化为缺项上三角算子矩阵的Fredholm补加以解决．

英文摘要：

Based on the closedness of range of the top right entry and the dimenmon perturbation of some family of spaces, a new necessary and sufficient condition is ob- tained for the partial block operator matrix （A？ CB） tO have a Fredholm completion. It is shown that this kind of completion problems can be reduced to the case of upper triangular operator matrices.