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On the random conjugate spaces of a random locally convex module

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Abstract

Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result: if the base (Ω, F, P) of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L 0-convex topology.

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Authors and Affiliations

  1. LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, 100191, P. R. China

    Tie Xin Guo & Shi En Zhao

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  1. Tie Xin Guo
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  2. Shi En Zhao
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Correspondence to Tie Xin Guo.

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Supported by National Natural Science Foundation of China (Grant No. 10871016)

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Guo, T.X., Zhao, S.E. On the random conjugate spaces of a random locally convex module. Acta. Math. Sin.-English Ser. 28, 687–696 (2012). https://doi.org/10.1007/s10114-011-0408-x

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  • DOI: https://doi.org/10.1007/s10114-011-0408-x

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