ON THE GENERALIZED RESOLVENT OF LINEAR PENCILS IN BANACH SPACES  

作　　者：Qianglian Huang Shuangyun Gao 

机构地区：[1]Yangzhou University, China

出　　处：《Analysis in Theory and Applications》2012年第2期146-155,共10页分析理论与应用（英文刊）

基　　金：Supported by the Natural Science Foundation of China (10971182);the Natural Science Foundation of Jiangsu Province (BK2010309);the Jiangsu Government Scholarship for Overseas Studies, the Natural Science Foundation of Jiangsu Education Committee (10KJB110012 and 11KJB110018);the Natural Science Foundation of Yangzhou University

摘　　要：. Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T - λS are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area.. Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T - λS are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area.

关 键 词：generalized inverse generalized resolvent linear pencils Moore-Penrose in-verse Fredholm operator semi-Fredholm operator 

分 类 号：O177.2[理学—数学] TP271.61[理学—基础数学]