摘要
当人们考察从黎曼流形到Hibert loop李群的映射时，会遇到一类到无穷维空间R^∞的映射．有关这类映射的一些基本性质不是很清晰，如著名的Arzela—Ascoli定理等．本文建立了Hilbert loop群映射空间的范数，得到了有界是致密集的充要条件，为进一步研究，如到Hilbert loop群的调和映射打下了基础．
People could be confronted with the mappings into R~∞ when they consider
the maps from Riemannian manifold into Hilbert loop Lie groups. However, some
properties of the maps, such as the renowned Arzela-Ascoli theorem, are not clear. We
shall give the norms of the space of the maps into Hilbert loop group, and prove the
Arzala-Ascoli theorem in this article.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2004年第3期607-614,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金(10371021)
关键词
无穷维李群
致密性
充要条件
Infinite dimensional Lie group
Compactness
Sufficient and necessary condition
