On some basic theorems of continuous module homomorphisms between random normed modules

DOI10.1155/2013/989102zbMath1295.46036OpenAlexW1985120553WikidataQ59012834 ScholiaQ59012834MaRDI QIDQ2443780

Tie-Xin Guo

Publication date: 8 April 2014

Published in: Journal of Function Spaces and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/989102

zbMATH Keywords

closed graph theoremopen mapping theoremrandom normed modulesmodule homomorphism

Mathematics Subject Classification ID

Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) (46A30)

Related Items (11)

Orthogonal decompositions in Hilbert \(A\)-modules ⋮ Hilbert \(A\)-modules ⋮ \(L^0\)-convex compactness and random normal structure in \(L^0(\mathcal{F}, B)\) ⋮ A characterization for a complete random normed module to be mean ergodic ⋮ Some results on random smoothness ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Two fixed point theorems in complete random normed modules and their applications to backward stochastic equations ⋮ A New Closed Graph Theorem on Product Spaces ⋮ L⁰-convex compactness and its applications to random convex optimization and random variational inequalities ⋮ Semigroups of continuous module homomorphisms on complex complete random normed modules

Cites Work

• The Bishop-Phelps theorem in complete random normed modules endowed with the (\(\varepsilon, \lambda\))-topology
• 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
• Separation and duality in locally \(L^0\)-convex modules
• A basic strict separation theorem in random locally convex modules
• A note on pointwise best approximation
• Pointwise best approximation in the space of strongly measurable functions with applications to best approximation in \(L^ p(\mu,X)\)
• Radon-Nikodým property of conjugate Banach spaces and \(w^*\)-equivalence theorems of \(w^*-\mu\)-measurable functions
• Representation theorems of the dual of Lebesgue-Bochner function spaces
• 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
• THE RANDOM SUBREFLEXIVITY OF COMPLETE RANDOM NORMED MODULES
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On some basic theorems of continuous module homomorphisms between random normed modules