关于概率赋范线性空间上的线性算子的一致收敛
On Uniform Convergence of Linear Operators on the Probabilistic Normed Space
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摘要: 本文引入了概率赋范线性空间上线性算子的一致收敛和可完全刻划这种收敛的算子间的概率距离概念,并利用这些概念获得了算子连续和算子列一致收敛的本质特征,及其连续性和全连续性对于一致收敛极限运算的封闭性.Abstract: In this paper, we introduced the notion of uniform convergence of the linear operators on the probabilistic nornied space, and the notion of probabilistic distance between the operators, which describes the above convergence completely. In terms of these notions, we obtained the essential features of the continuity of operators, and of the uniform convergence of operator sequences, and we also obtained the closure of continuity and complete continuity under the operation of the limit of uniform convergence.
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[1] Radu, V, C, R,Acade, Sci,Paris, 280 (1975), 80-89. [2] 林熙,概率赋范线性空间中的线性算子,工程数学学报,4,(1987), 43-43. [3] 龚怀云、张敏先、刘作述,概率度量空间的有界性、可分性与紧性,工程数学学报,1,2(1984), 57-66. [4] 龚怀云,概率度量空间的概率列紧性,工程数学学报,创刊号(1984), 76-80. [5] 游兆永、龚怀云、朱林户、林熙,试论概率赋范空间上的线性算子及其他,第四届全国泛函分析会议论文(1986), 1-10. [6] 张石生,《不动点理论及其应用》,重庆出版社(985), 417-488. -
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