算子概率范数与共鸣定理

Probabilistic Norm of Operators and Resonance Theorems

1.
Department of Mathematics, Yancheng Educational Institute, Yancheng, Jiangsu 224002, P R China;
2.
Department of Mathematics, Yancheng Teachers College, Yancheng, Jiangsu 224002, P R China

摘要: 提出概率赋范线性空间上集合有界性的简化定义,利用算子概率范数概念。进一步研究概率赋范线性空间上的线性算子理论,并在算子概率赋范空间上,建立了概率有界、概率半有界、非概率无界意义下的共鸣定理。
- 概率范数 /
- 概率有界集 /
- 非概率无界集 /
- 共鸣定理
Abstract: In this paper,a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced.By means of the probabilistic norm of linear operators,the linear operator theory on probabilistic normed linear space was further studied.On probabilistic normed linear operator space,some resonance theorems dealing with probabilistic bounded sets,probabilistic semi-bounded sets,and probabilistic non-unbounded sets are obtained.
- probabilistic norm /
- probabilistic bounded set /
- probabilistic non-unbounded set /
- resonance theorem

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