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Random duality

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Abstract

The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.

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Authors and Affiliations

  1. Key Laboratory of Information Mathematics and Behavior, Ministry of Education, Department of Mathematics, Beihang University, Beijing, 100191, China

    TieXin Guo

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    TieXin Guo & XinXiang Chen

Authors
  1. TieXin Guo
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  2. XinXiang Chen
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Correspondence to TieXin Guo.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10871016)

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Guo, T., Chen, X. Random duality. Sci. China Ser. A-Math. 52, 2084–2098 (2009). https://doi.org/10.1007/s11425-009-0149-9

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  • DOI: https://doi.org/10.1007/s11425-009-0149-9

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