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.
出处
《数学的实践与认识》
CSCD
北大核心
2008年第9期187-192,共6页
Mathematics in Practice and Theory
