拓扑线性空间中线性算子的左拓扑内逆的判据

Criteria of left topological inner inverse of linear operator intopological linear space

针对M.Z.Nashed等为拓扑线性空间中线性算子引入的左拓扑内逆的概念存在的不便于应用的缺陷,给出M.Z.Nashed等所定义的线性算子的左拓扑内逆的一组等价的判别条件,并加以证明。由此引入在一般线性拓扑空间中线性算子左拓扑内逆的便于应用的新定义。该定义对研究拓扑空间中线性算子的拓扑内逆具有重要意义。

It is well known that there always exists an algebraic inner inverse of a linear operator between linear spaces, but the topological inner inverse for a linear operator between topological linear spaces dose not always exist. The paper introduces the concept of the left topological inner inverse for a linear operator topological space, as defined by M. Z. Nashed etc. But it is not convenient for this definition to be applied. This paper gives a group of simple convenient condition for the left topological inner inverse introduced by M. Z. Nashed etc. and then prove them. It follows that a new definition for the left topological inner inverse is introduced in the end. And this definition is very important for us to study the topological inner inverse for a linear operator in a topological spaces.