On probabilistic norm of a linear operators and space of operators

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. Foundation item: the National Natural Science Foundation of Educational Committee of Jiangsu Province of China (JW970135)