全连续算子的固有值、固有元的全局特征和应用  

THE GLOBAL CHARACTERISTICS AND APPLICATION OF EIGENVALUE AND EIGENELEMENT ON THE COMPLETELY CONTINUOUS OPERATOR

作　　者：赵从江[1] 

机构地区：[1]中国民航飞行学院基础部

出　　处：《纯粹数学与应用数学》1998年第3期65-71,共7页Pure and Applied Mathematics

摘　　要：仅分别在‖Ａｘ‖‖ｘ‖→＋∞（‖ｘ‖→＋∞）和‖Ａｘ‖‖ｘ‖→＋∞（‖ｘ‖→０）之下，研究全连续算子的固有值、固有元的某种全局特征，并应用到Ｈａｍｍｅｒｓｔｅｉｎ算子的研究上，得到了新的结果．This paper studies some global characteristics of eigenvalue and eigenelement on the completely continuous operator under the only ‖Ax‖‖x‖→+∞(‖x‖→+∞) and the ‖Ax‖‖x‖→+∞(‖x‖→0), respectively. Furthermore, we utilize our results to study the global characteristics of eigenvalue and eigenfunction of the Hammerstein operator, and some new results are obtained.

关 键 词：全连续算子 全局特征 固有值 固有元 巴拿赫空间 

分 类 号：O175.9[理学—数学]