四川大学学报（自然科学版）2008，Vol.45Issue(1)：33-34,2.
Hilbert空间就范直交系的完备性
On the completenes of an orthonormal set
邓荣春 1钟昌勇2
作者信息
- 1. 四川大学数学学院,成都,610064
- 2. 佐治亚州立大学数学,与统计学系,亚特兰大,3965,美国
- 折叠
摘要
Abstract
A criterion on the completeness of an orthonormal set in a Hilbert space presented. The new criterion which extends Birhoff and Rotas result is in terms of the compactness of an operator on a Hilbert space. Birhoff and Rotas criterion, if restated in the language of operator theory, is assuming the trace class membership of the corresponding operator. The approach presended in this paper, which involves Fredholm theory, avoids all the computations as presented in Birhoff and Rotas original proof and then simplified by Tsao.关键词
完备性/Hilbert空间/Fredholm理论/就范直交系Key words
completeness, Hilbert space, Fredolm theory, orthonormal set分类
数理科学引用本文复制引用
邓荣春,钟昌勇..Hilbert空间就范直交系的完备性[J].四川大学学报（自然科学版）,2008,45(1):33-34,2.
