Random duality

DOI10.1007/s11425-009-0149-9zbMath1193.46048OpenAlexW3191102628MaRDI QIDQ1047832

Xin Xiang Chen, Tie-Xin Guo

Publication date: 6 January 2010

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-009-0149-9

zbMATH Keywords

random normed modulesstratification structurerandom duality theory

Mathematics Subject Classification ID

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) General theory of topological algebras (46H05) Duality theory for topological vector spaces (46A20) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Functional analysis in probabilistic metric linear spaces (46S50)

Related Items (10)

On the random conjugate spaces of a random locally convex module ⋮ The embedding theorem of an \(L^0\)-prebarreled module into its random biconjugate space ⋮ The relations among the three kinds of conditional risk measures ⋮ THE RANDOM SUBREFLEXIVITY OF COMPLETE RANDOM NORMED MODULES ⋮ Random spectral theorems of self-adjoint random linear operators on complete complex random inner product modules ⋮ Relations between some basic results derived from two kinds of topologies for a random locally convex module ⋮ Recent progress in random metric theory and its applications to conditional risk measures ⋮ Randomized versions of Mazur lemma and Krein-Smulian theorem ⋮ Random strict convexity and random uniform convexity in random normed modules ⋮ L⁰-convex compactness and its applications to random convex optimization and random variational inequalities

Cites Work

• The James theorem in complete random normed modules
• Several applications of the theory of random conjugate spaces to measurability problems
• A basic strict separation theorem in random locally convex modules
• A note on pointwise best approximation
• Radon-Nikodým property of conjugate Banach spaces and \(w^*\)-equivalence theorems of \(w^*-\mu\)-measurable functions
• A characterization of continuous module homomorphisms on random semi-normed modules and its applications
• Representation theorems of the dual of Lebesgue-Bochner function spaces
• The relation of Banach--Alaoglu theorem and Banach--Bourbaki--Kakutani--Šmulian theorem in complete random normed modules to stratification structure
• A characterization for an \(L(\mu,K)\)-topological module to admit enough canonical module homomorphisms
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