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In order to investigate the generalized Bott-Duffin inverse of A with respect to a closed subspace M on a infinite dimensional Hilbert space,the technique of block operator matrix is aplied,its representations and its property are investigated.

运用算子分块的理论,使算子的广义Bott-Duffin逆的结构更加清晰化,便于研究它的表示及性质,主要给出了算子的广义Bott-Duffin逆的精确的表示形式。

Gudder got in(4),we give a wholely new proof by the technique of block operator matrix which makes the geometry structure of operators more clear.

Gudder在文献〔4〕中所得到的结果,本文利用算子分块的技巧给出了全新的证明过程,使算子的几何结构更加清晰。