Nonexpansive projections on subsets of Banach spaces.
Nonexpansive projections on subsets of Banach spaces.
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DOI：
10.2140/pjm.1973.47.341
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发表时间：
1973-08
影响因子：
0.6
通讯作者：
Ronald E. Bruck
中科院分区：
文献类型：
--
作者：
Ronald E. Bruck
如果C是Banach空间E的凸子集，则投影是C到子集F上的收缩r，对于每个x e C，它将射线{r（x）+ t（x-r（x））：t ^ 0}<$C的每个点映射到同一点r（x）上。收缩r称为正交的，如果对于每个x，x-r（x）在与R相关的意义上垂直于F。C. James.本文建立了三个主要结果。
If C is a convex subset of a Banach space E, a projection is a retraction r of C onto a subset F which for each x e C maps each point of the ray {r(x) + t(x — r(x)): t ^ 0} Π C onto the same point r(x). A retraction r is said to be orthogonal if for each x, x — r(x) is normal to F in a sense related to that of R. C. James. This paper establishes three main results.