摘要
本文证明了在平移空间上可利用距离在一定条件下构作出线性结构,引入了次范整线性空间的概念,还证明了平移空间是次范整线性空间当且仅当它的平移群是Abel群.泛函分析学中的有界线性算子定理,Hahn-Banach定理以及共鸣定理都可以移植于次范整线性空间之中.
It is proved that linear structures can be constructed by means of metrics on translation spaces under certain conditions. The concept of sub-normed Z-linear spaces is introduced and it is clarified that a translation space is a sub-normed Z-linear space if and only if its translation group is Abelian. Analogues the bounded linear operator theorem, the Hahn-Banach theorem and the resonance theorem are established in sub-normed Z-linear space.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2005年第1期1-10,共10页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金重点资助项目(10331010)
