The Best Bounded Quasi-linear Generalized Inverse of the Linear Operator in Bnanch Spaces

摘要：

Let X,Y be Banach spaces, T be a linear operator from X to Y. The bounded quasi-linear generalized inverse Th (which, itself is an extension of matrix generalized inverse, the single-valued metric generalized inverseTM, and the continuous linear projector generalized inverseT+) of the linear operator T in arbitrary Banach spaces is investigated, If X and Y are reflexive, we prove that the set of all bounded quasi-linear generalized inverse of T is not empty. In Banach space of all bounded homogeneous operators, the best bounded quasi-linear generalized inverseTh of T is just the Moore-Penrose metric generalized inverseTM.These results indeed extend and improve the corresponding work done by P. Liu and Y. W. Wang in 2007from reflexive and strictly convex Banach spaces to the general Banach spaces.

关键词： bounded quasi-linear generalized inverse ezistence characterization linear operator

作者: Renxing Ni

作者单位: Department of Mathematics, Shaoxing University, Zhejiang 312000, P.R.China

会议类型: 国际会议

会议名称: The Third International Workshop on Applied Matriz Theory(第三届国际矩阵分析与应用会议)

会议地点: 杭州

会议语种:英文

页码: 874-877

在线出版日期: 2009-07-09（万方平台首次上网日期，不代表论文的发表时间）