Banach空间中Birkhoff正交性的刻画  

Characterizations of Birkhoff Orthogonality in Banach Space

作　　者：杨冲[1] 张登华[2] 

机构地区：[1]华北电力大学数理系,河北保定071003 [2]华北电力大学科技学院,河北保定071003

出　　处：《数学的实践与认识》2008年第9期187-192,共6页Mathematics in Practice and Theory

摘　　要：研究了Banach空间中两元素a和b在Birkhoff意义下正交的性质,给出在Banach空间中两个元素B-正交和线性泛函的关系,然后用线性泛函来研究B-正交性与Banach空间的可微性、凸性、自反性的关系.本文最后定义B-正交性的补,通过B-正交性的补来研究B-正交性和Banach空间的性质.We discuss some propositions of a to be orthogonal to b in the sense of Birkhoff in a Banach space X. And we give the relations of B-orthogonality with linear functional, then use linear functional to discuss Gateaux differentiability, convexity and reflexivity in a Banach space. Last, we define B-complementary subspace, and dicuss some propositions of it.

关 键 词：Birkhoff正交性 Gateaux可微性 线性泛函 自反空间 

分 类 号：O177[理学—数学]