关于算子方程Tx=y扰动分析的一些结果

在Banach空间中给出了一种相容算子方程解的误差估计 ,推广了矩阵扰动分析中的相应结果 .此外 ,利用Hilbert空间中算子M -P广义逆与算子的约化极小模之间的关系 ,给出了一些估计式 ,这些估计式对于分析不相容算子方程Tx =y的极小范数最小二乘解的扰动误差是有用的

Some results about the perturbation analysis for the operator equation Tx=y

This paper consists of two parts. In part 1,the error estimates for operator equation Tx=y where T -1 exists are given in Banach spaces, which generalizes the corresponding results in the matrix perturbation analysis. In part 2,by use of the relation between the M-P generalized inverse of T and the reduced minimum module, some estimates are given. The result provided here is useful to perturbation analysis for the minimum norm least squares solution to the operator equation Tx=y in Hilbert spaces.