两个幂等算子线性组合的Drazin逆(英文)

The Drazin Inverse of the Linear Combination of Two Idempotents

设P和Q是希尔伯特空间H上的幂等算子,且非零复数c1,c2满足c1,c2∈\C{0}.利用算子分块技巧,分别讨论了在PQP=0、PQP=P和PQP=PQ条件下,线性组合c1P+c2Q的Drazin逆表达式.

Let P and Q be idempotent on H. For any given c1,c2∈ ／cC{O} satisfying c1 ＋c2 ≠0 ,the representations for the Drazin inverse of c1P＋ c2Q under some conditions such as PQP =0, PQP= P and PQP = PQ are obtained by using the technique of block operator matrices respectively.