幂等算子的Moore-Penrose逆

Moore-Penrose Inverses of Idempotent Operators

考虑无限维Hilbert空间上幂等算子的Moore-Penrose逆的表示。利用算子分块的技巧,得到了幂等算子的一个矩阵刻画,给出了幂等算子的Moore-Penrose逆的一个矩阵表示。

The Moore-Penrose inverse of the idempotent operator on the Hilbert space of infinite dimensional was studied. The characterization of the idempotent operator was provided through the technique of operator block, and an explicit representation of the Moore-Penrose inverse of the idempotent operator was presented as well.