Hilbert空间中—广义幂等算子方程的解

Solutions of Some Generalized Idempotent Operator Equations in the Hilbert Space

设算子A是无限维Hilbert空间上的一个广义幂等算子,利用广义幂等算子A在特定空间分解下的矩阵形式,对一类算子方程的解与自伴解进行研究,并给出该算子方程的解和自伴解的一般表达式.

To let A is a generalized idempotent operator in the Infinite Dimensional Hilbert Space, using the block operator matrix technique in the space decomposition, we give the sufficient and necessary conditions for the existence of solutions of the equation and the representations of those solutions.