Banach空间中线性流形上的度量投影的表达式

借助于正规对偶映射,建立了一般Banach空间中线性流形上的(集值)度量投影存在的 充要条件,同时给出了度量投影的表达式和点到线性流形上的距离公式.这些本质地推广和改进了 王玉文和于金凤在空间自反、严格凸和光滑强假定下的相应结果.

The Representive of Metric Projection on the Linear Manifold in Arbitary Banach Space

This paper established the necessary and sufficient condition for existence of (set-valued) metric projection on the linear manifold in arbitary Banach space by the normalized duality mapping. Meanwhile, a representive of metric projection on the linear manifold in arbitary Banach space was given, so was the distance formulas from a point to the linear manifold in Banach space. These indeed extended and improved the corresponding results obtained by Wang Yuwen and Yu Jinfeng under the strong assumption that the space X was a reflexive, smooth and strictly convex Banach space.