Banach空间中一类集值度量广义逆的连续线性选择

The Linear Continuous Selection of a Class of Set-valued Metric Generalized Inverse in Banach Space

对于Banach空间中余一维闭值域有界线性算子的集值度量广义逆,给出其具有连续线性选择的充分必要条件.结果是对M.Z.Nashed与G.F.Votruba提出的研究问题的部分回答.

We discuss the problem of the set-valued metric generalized inverse of bounded linear operator with 1-codimensioned closed range in Banach space. And we prove the necessary and sufficient conditions of the set-valued metric generalized inverse with linear continuous selection. And our results partially solved the research problem raised by M. Z. Nashed and G. F. Votruba in .