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

• Articles • Previous Articles     Next Articles

ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS

Fang Jinxuan   

  1. 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)

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

2010 MSC Number: 

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