Abstract
Abstract The idempotent operator in Hilbert space can be decomposed into a linear combination of two idempotent operators, and two idempotent operators are obtained through the decomposition process. The Drazin inverse representation of the linear combination of idempotent operators based on space decomposition is researched in this paper. By using the block operator matrix technique, the infinite-dimensional complex Hilbert space is decomposed to obtain the expression of the Drazin inverse of two idempotent operators P and Q’s multilinear combinations under different conditions.
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