摘要
紧算子理论是算子理论和泛函分析的重要内容。紧算子理论的思想起源可以追溯到二次型主轴化的代数理论。希尔伯特在建立无穷二次型的谱理论时提出了全连续概念,里斯用现代算子语言重新表述希尔伯特的这一概念而给出了紧算子的定义,并建立了紧算子理论,其成果可以推广到抽象巴拿赫空间上进而建立起巴拿赫空间上的紧算子理论。对紧算子理论的思想起源、演变及形成过程进行研究可以使我们更好地理解算子理论和泛函分析的历史发展过程。
Compact operator theory is the important content of operator theory and functional analysis. The idea of compact operator theory stemmed fi＇om the algebra theory on reduction of quadratic forms. Hilbert proposed the concept of completely eontinuous in his work on spectral theory of infinite quadrat- ic forms, Riesz reformulated Hilbert＇ s concept in the language of modern operator and gave the definition of compact operator, and he established his compact operator theory. Riesz＇ s results can be extended to abstract Banach space, thus compact operator theory on Banach space was obtained. The historical exploring on the origin, evolution and development of compact operator theory can help us to better understand the history of operator theory and functional analysis.
出处
《自然辩证法研究》
CSSCI
北大核心
2014年第12期80-84,共5页
Studies in Dialectics of Nature
基金
国家自然科学基金资助项目(11171271
11326048)
中国博士后科学基金资助项目(2013M532079
2014T70932)
西北大学科学研究基金资助项目(12NW04)
关键词
紧算子
泛函分析
积分方程
希尔伯特
Compact operator
functional analysis
integral equation
David Hi｜bert
