论文标题
一般巴拉赫空间的普遍预测
Generalized projections on general Banach spaces
论文作者
论文摘要
总的来说，巴纳克空间，公制投影图缺少其在希尔伯特空间中所拥有的强大特性。为了解决公制投影的许多缺陷，已经提出了一些广义预测。但是，这种概念主要是在具有丰富拓扑结构的Banach空间中进行的，例如均匀凸出的Banach空间。在本文中，我们研究了普通巴拉奇空间中的两个广义投影概念。提供了各种示例，以证明拟议的概念和从特殊结构化的Banach空间迁移到一般Banach空间后的广义预测中的结构丧失。彻底探索了广义投影与度量投影之间的连接。
In general Banach spaces, the metric projection map lacks the powerful properties it enjoys in Hilbert spaces. There are a few generalized projections that have been proposed in order to resolve many of the deficiencies of the metric projection. However, such notions are predominantly studied in Banach spaces with rich topological structures, such as uniformly convex Banach spaces. In this paper, we investigate two notions of generalized projection in general Banach spaces. Various examples are provided to demonstrate the proposed notions and the loss of structure in the generalized projections after migrating from specially structured Banach spaces to general Banach spaces. Connections between the generalized projection and the metric projection are thoroughly explored.
