集值度量广义逆的存在性

Existence of Set-valued Metric Generalized Inverses

设X,Y为Banach空间,T∈L(X,Y)为从X到Y的线性算子,D(T),N(T),R(T)分别为T的定义域,核空间与值域,使用算子T的自身性质,给出T具有集值度量广义逆T和R(T)D(T)的充分必要条件.

Let X,Y be Banach spaces, T ∈L（X,Y） be a linear operator from X to Y,D（T）, N（T） and R（T） be the domain null space and range of T respectively, By means of the property of T we give a necessary and sufficient conditron for the set-valued metric generalized inverse T^e of T to exist.