摘要
研究Hilbert空间上幂等算子的Drazin逆等价性性质。引入Hilbert空间上有界线性算子的空间分解理论和算子矩阵分块的技巧,给出幂等算子在一定空间分解下的算子矩阵表示,进而研究幂等算子和、差和积的Drazin逆的几个等价条件,最后给出幂等算子积条件下Drazin逆的等价条件。
Properties of two idempotent operators on a Hilbert space are studied.Based on the theory of space decomposition of linear and bounded operators and the technique of operator matrix blocking, the representations and characterization of two idempotent operators on a given Hilbert space are given. And several equivalent conditions for the Drazin invertibility of the sum, difference of two idempotents on a Hilbert space are studied. Furthermore, equivalent condition for the Drazin invertibility of the product of idempotents is obtained.
引文
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