线性算子在商空间上的诱导算子的若干性质  

Some Properties of Deduced Operator on Quotient Space by a Linear Operator

作　　者：任蕴丽[1] 郭雅彩[1] 阎欣华[2] 樊丽丽[3] 

机构地区：[1]河北科技师范学院数理系,河北秦皇岛066004 [2]北京石油化工学院数理系 [3]唐山师范学院数学与信息科学系

出　　处：《河北科技师范学院学报》2009年第1期34-36,共3页Journal of Hebei Normal University of Science & Technology

基　　金：唐山师范学院自然科学研究发展基金项目(项目编号:07C21)

摘　　要：论证了线性算子f在模f的核的商空间上所诱导的算子保持f的有界性及闭性,Banach空间上满的线性算子f所诱导的算子T:X/X0→X/f(X0)保持f的紧性,并且当f为线性同构时,T是线性同胚映射。In this paper, it is proved that the operator deduced on the quotient space moduled by the kernel of a linear operator f preserves the boundedness and closedness of f, and that the operator T： X/X0→X/f（X0） deduced by a surjective linear operator f on a Banach space preserves the compactness of f and T is homeomorphic if f is isomorphic.

关 键 词：赋范线性空间 商空间 线性算子 

分 类 号：O177.3[理学—数学]