ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS

Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (10): 1160-1166.

ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS

方锦暄

Department of Mathematics, Nanjing Normal University, Nanjing 210097, P.R.China

收稿日期:1997-12-12 修回日期:1998-04-21 出版日期:1999-10-18 发布日期:1999-10-18
通讯作者: Zhang Shisheng
基金资助:
the National Natural Science Foundation of Educational Committee of Jiangsu Province of China ( JW970135)

ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS

Fang Jinxuan

Department of Mathematics, Nanjing Normal University, Nanjing 210097, P.R.China

Received:1997-12-12 Revised:1998-04-21 Online:1999-10-18 Published:1999-10-18
Supported by:
the National Natural Science Foundation of Educational Committee of Jiangsu Province of China ( JW970135)

摘要/Abstract

摘要： Since the PN space (E,F) which satisfies condition (PN-5) is just a Menger PN-space (E,F,min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PN-spaces. The results presented improve and generalize the corresponding results by Xiao.

关键词: probabilistic normed space, probabilistic norm of a linear operator, space of operators

Abstract: Since the PN space (E,F) which satisfies condition (PN-5) is just a Menger PN-space (E,F,min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PN-spaces. The results presented improve and generalize the corresponding results by Xiao.

Key words: probabilistic normed space, probabilistic norm of a linear operator, space of operators

中图分类号:

O177.99

方锦暄. ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(10): 1160-1166.

Fang Jinxuan . ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(10): 1160-1166.

[1]	张石生;陈玉清. NONLINEAR SEMIGROUPS AND DIFFERENTIAL INCLUSIONS IN PROBABILISTIC NORMED SPACES[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(9): 815-829.
[2]	张石生;彭永成. PROBABILISTIC CONTRACTOR COUPLE AND SOLUTIONS FOR A SYSTEM OF NONLINEAR EQUATIONS IN NON-ARCHIMEDEAN MENGER PROBABILISTIC NORMED SPACES[J]. Applied Mathematics and Mechanics (English Edition), 1991, 12(11): 1031-1038.
[3]	张石生;陈玉清. ON THE EXISTENCE OF SOLUTIONS FOR EQUATIONS WITH ACCRETIVE MAPPINGS IN PROBABILISTIC NORMED SPACES[J]. Applied Mathematics and Mechanics (English Edition), 1990, 11(9): 821-828.

ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS

ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS

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