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| 线性算子在商空间上的诱导算子的若干性质 | |
| 引用本文： | 任蕴丽,郭雅彩,阎欣华,樊丽丽.线性算子在商空间上的诱导算子的若干性质[J].河北科技师范学院学报,2009,23(1):34-36. |
| 作者姓名： | 任蕴丽 郭雅彩 阎欣华 樊丽丽 |
| 作者单位： | 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 |
| 基金项目： | 唐山师范学院自然科学研究发展基金 |
| 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。 |
| 关 键 词： | 赋范线性空间 商空间 线性算子 |
Some Properties of Deduced Operator on Quotient Space by a Linear Operator |
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| REN Yun-li,GUO Ya-cai,YAN Xin-hua,FAN Li-li.Some Properties of Deduced Operator on Quotient Space by a Linear Operator[J].Journal of Hebei Normal University of Science & Technology,2009,23(1):34-36. | |
| Authors: | REN Yun-li GUO Ya-cai YAN Xin-hua FAN Li-li |
| Institution: | 1 Dept of Mathematics & Physics;Hebei Normal University of Science & Technology;Qinhuangdao Hebei;066004;2 Beijing Institute of Petro-Chemical Technology;3 Tangshan Teachers College;China |
| Abstract: | 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. |
| Keywords: | normed linear space quotient space linear operator |
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