Generalized projections, decompositions, and the Pythagorean-type theorem in Banach spaces

被引：14

作者：

Alber, YI ^{[1
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

APPLIED MATHEMATICS LETTERS | 1998年 / 11卷 / 06期

关键词：

Banach spaces; duality mappings; generalized projection operators; dual and polar cones; basic variational principle for generalized projections; Lyapunov functionals; Young-Fenchel transformation;

D O I：

10.1016/S0893-9659(98)00112-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate new properties of the generalized projection operators on convex closed cones in uniformly convex end uniformly smooth Banach spaces; establish decompositions theorems for arbitrary elements both in primary and dual spaces; and prove the Banach space analogue of the Pythagorean-type theorem. Earlier, all these results were known only in Hilbert spaces. (C) 1998 Elsevier Science Ltd. All rights reserved.

引用

页码：115 / 121

页数：7