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中文摘要：
研究了Douglas方程解的几何结构,利用算子分块的方法,得到了Douglas方程的约化解和自伴解的算子矩阵表示,并对Arias,Corach及Gonzalez等人的部分结果给出了不同的证明.结果表明,在相应的空间分解下,算子方程BX=C关于子空间M的约化解XM和自伴解X的算子矩阵形式分别为XM=BM-1C1100 0,X=B1-1C1B1-1C2（B1-1C2）＊X4,而且方程的正解存在的一个充分必要条件是BB′C=C,BC＊∈B（K）自伴,B1-1C1是正算子,R（B1-1C2）R（（B1-1C1）12）.
英文摘要：
The geometrical structure of Douglas equations are studied.By using the technique of block operator,the operator matrix representations of the reduced solutions and the hermitian solutions of the operator equation BX=C are obtained and the alternative proofs of some results given by Arias,Corach and Gonzalez are also given.The results show that,under the corresponding space decompositions,the reduced solution XM with respect to the subspace M and the hermitian solution X of the operator equation BX=C have the operator matrix forms XM=（B-1MC11000）,X=（B-11C1B-11C2（B-11C2）＊X4）,respectively.Moreover,a necessary and sufficient condition for the existence of the positive solution of the equation is that BB′C=C,BC＊∈B（K）is self-adjoint,B-11C1 is positive,and R（B-11C2）R（（B-11C1）1/2）.
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