THE RANDOM SUBREFLEXIVITY OF COMPLETE RANDOM NORMED MODULES

DOI10.1142/S0129167X12500474zbMath1253.46080OpenAlexW2065073991MaRDI QIDQ5389540

Shien Zhao, Tie-Xin Guo

Publication date: 21 April 2012

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x12500474

zbMATH Keywords

random normed modulelocally \(L^{0}\)-convex topologycountable concatenation property\((\epsilon\lambda )\)-topologyrandom subreflexivity

Mathematics Subject Classification ID

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 (6)

The embedding theorem of an \(L^0\)-prebarreled module into its random biconjugate space ⋮ Unnamed Item ⋮ The Bishop-Phelps theorem in complete random normed modules endowed with the (\(\varepsilon, \lambda\))-topology ⋮ Various expressions for modulus of random convexity ⋮ An exponential representation for random C₀–semigroups ⋮ On some basic theorems of continuous module homomorphisms between random normed modules

Cites Work

• The algebraic structure of finitely generated \(L^0(\mathcal F, K)\)-modules and the Helly theorem in random normed modules
• Recent progress in random metric theory and its applications to conditional risk measures
• The James theorem in complete random normed modules
• Subreflexive normed linear space
• Relations between some basic results derived from two kinds of topologies for a random locally convex module
• Separation and duality in locally \(L^0\)-convex modules
• A basic strict separation theorem in random locally convex modules
• Random duality
• Continuity properties of probabilistic norms
• A characterization of continuous module homomorphisms on random semi-normed modules and its applications
• Probabilistic norms and convergence of random variables
• Extension theorems of continuous random linear operators on random domains
• The relation of Banach--Alaoglu theorem and Banach--Bourbaki--Kakutani--Šmulian theorem in complete random normed modules to stratification structure
• A proof that every Banach space is subreflexive

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