Banach空间中多值线性算子的集值度量广义逆及其单值选择

The Set-Valued Metric Generalized Inverses and Its Single-Valued Selection of Multi-Valued Linear Operator in Banach Spaces

本文利用Banach空间几何方法,特别是运用广义正交分解定理,给出了自反Banach空间中多值闭线性算子的集值度量广义逆的定义域、值域、表达式的精确表示.同时,给出了该度量广义逆的单值齐性选择的构造方法及其特征刻画,使得近期一些相关研究成果,可成为其直接推论.

In this paper,the exact representation of domain,range and expression of the set valued metric generalized inverse from the multi-valued closed linear operators in the inverse Banach spaces are given by means of the Banach spaces geometry method,especially the generalized orthogonal decomposition theorem.At the same time,the construction method and characterization of the single valued homogeneity selection of the metric generalized inverse are given,which makes some rencent related achievements can be deduced directly.