On the normability of generalized Šerstnev PN spaces |
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| Authors: | Gaoxun Zhang Minxian Zhang |
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| Affiliation: | aTian Fu College of Southwestern University of Finance and Economics, Mianyang, Sichuan 621000, PR China;bDepartment of Computation Science, Chengdu University of Information Technology, Chengdu, Sichuan 610225, PR China |
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| Abstract: | Probabilistic Normed spaces have been redefined by C. Alsina, B. Schweizer and A. Sklar. But even today, whether the generalized Šerstnev PN space is normable or not is still an open question. In this paper, through applying Kolmogorov's theorem, we will give several sufficient conditions, under which many generalized Šerstnev PN spaces are normable. As the application of our results, we will give two examples which are normable generalized Šerstnev PN space, but not Šerstnev space. |
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| Keywords: | Topologically bounded Locally convex Normability |
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