Banach空间中线性流形的单值度量投影算子部分

刘晶和王玉文于2001年引入并研究了Banach空间中线性流形的单值度量投影算子部分，但他们是在空间X和Y均自反、严格凸的强几何假定下来进行讨论的，这极不利于应用．我们在X和Y均是一般Banach空间的弱假定下，讨论并研究了Banach空间中线性流形的单值度量投影算子部分，并给出了该算子部分的结构的刻划．这为将比Lee S.J.与Nashed M.Z.所引进并研究的Hilbert空间集值线性映射包含的最小二乘解推广到Banach空间奠定了理论基础，所得的本质地推广了刘晶与王玉文的结果。

The Single-Valued Metric Operator Part of Linear Manifold in Banach Spaces

Liu Jing and Wang Yuwen (2001) introduce and inverstigate the single - valued metric operator part of linear manifold in Banach spaces. But their discussion is on the strong assumption that the spaces X and Y are reflexive and strictly convex, which is unfit for application. Now we discuss and inverstigate the single - valued metric operator part of linear manifold in Banach spaces on the weak assumption that the spaces X and Y are general Banach spaces. Moreover, the single - valued metric operator part in Banach space is structured. We investigate the least -squares solutions of set - valued linear mapping inclusion introduced and investigated by Lee S. J. and Nashed M. Z. from Hilbert spaces to Banach space. These indeed extend and generalize the recent results obtained by Liu Jing and Wang Yuwen.