The Bishop-Phelps theorem in complete random normed modules endowed with the (\(\varepsilon, \lambda\))-topology

DOI10.1016/j.jmaa.2012.02.037zbMath1245.46059OpenAlexW1966538382MaRDI QIDQ412477

Mingzhi Wu

Publication date: 4 May 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.02.037

zbMATH Keywords

Bishop-Phelps theoremrandom normed module\((\varepsilon, \lambda)\)-topologyclosed \(L^{0}\)-convex set

Mathematics Subject Classification ID

Functional analysis in probabilistic metric linear spaces (46S50)

Related Items (14)

The embedding theorem of an \(L^0\)-prebarreled module into its random biconjugate space ⋮ A characterization for a complete random normed module to be mean ergodic ⋮ Some results on random smoothness ⋮ Unnamed Item ⋮ Various expressions for modulus of random convexity ⋮ An exponential representation for random C₀–semigroups ⋮ A minimax theorem for \(\overline{L}^0\)-valued functions on random normed modules ⋮ On some basic theorems of continuous module homomorphisms between random normed modules ⋮ \(L^0\)-linear modulus of a random linear operator ⋮ Farkas' lemma in random locally convex modules and Minkowski-Weyl type results in \(L^0(\mathcal F,R^n)\) ⋮ On almost surely bounded semigroups of random linear operators ⋮ Two fixed point theorems in complete random normed modules and their applications to backward stochastic equations ⋮ L⁰-convex compactness and its applications to random convex optimization and random variational inequalities ⋮ On non-\(L^0\)-linear perturbations of random isometries in random normed modules

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Recent progress in random metric theory and its applications to conditional risk measures
• The James theorem in complete random normed modules
• Ekeland's variational principle for an \(\overline{L}^0\)-valued function on a complete random metric space
• Relations between some basic results derived from two kinds of topologies for a random locally convex module
• A basic strict separation theorem in random locally convex modules
• Representation theorems of the dual of Lebesgue-Bochner function spaces
• Probabilistic norms and convergence of random variables
• Extension theorems of continuous random linear operators on random domains
• A short and partial history of probabilistic normed spaces
• A proof that every Banach space is subreflexive
• THE RANDOM SUBREFLEXIVITY OF COMPLETE RANDOM NORMED MODULES
• A study of boundedness in probabilistic normed spaces

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