Banach空间中线性算子的(集值)度量广义逆的表示及应用

THE REPRESENTATION OF THE SET-VALUED METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE AND ITS APPLICATION

在Banach空间Y无自反和从Banach空间X到Y的线性算子T无闭值域和稠定的假定下,利用Banach空间几何方法证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,建立了该度量广义逆的存在性、唯一性和等价表达式,并给出了此表达式的一个应用示例．所得的部分结果本质地拓广王玉文和潘少荣在Banach空间Y自反,从X到Y的线性算子T为闭值域和稠定的假定下的近期相应结果．

Without the assumption that Banach space Y is reflexive and T is a densely defined linear operator with closed range from Banach space X to Y, it is proved that the metric generalized inverse of linear operator has closed convex range set-valued mapping by means of geometry of Banach space. Existence, uniqueness and the equivalent representation of the metric generalized inverse are established, and an application example of the representation is given. Parts of our results have extended and improved the corresponding recent results obtained by Wang Yu-wen and Pan Shao-rong under the above-mentioned assumption.