\(L^0\)-linear modulus of a random linear operator
type: Item
instance of: scholarly article
title: \(L^0\)-linear modulus of a random linear operator
zbMATH Open document ID: 1472.47028
DOI: 10.1155/2014/183197
author: Ming Liu
author: Xia Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We prove that there exists a unique \(L^0\)-linear modulus for an a.s.\ bounded random linear operator on a specifical random normed module, which generalizes the classical case.
Mathematics Subject Classification ID: 47B80
zbMATH DE Number: 7021889
zbMATH Keywords: \(L^0\)-linear modulus
zbMATH Keywords: bounded random operator
zbMATH Keywords: random normed module
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/183197
OpenAlex ID: W2075486781
Wikidata QID: Q59035848
cites work: Linear Modulus of a Linear Operator
cites work: Majorizing Operators between $L^p$ Spaces and an Operator Extension of Lebesgue's Dominated Convergence Theorem.
cites work: Ergodic theorems for contraction semigroups
cites work: Contraction semigroups in Lebesgue space
cites work: Subadditive mean ergodic theorems
cites work: On mean ergodic semigroups of random linear operators
cites work: On conditional mean ergodic semigroups of random linear operators
cites work: Von Neumann's mean ergodic theorem on complete random inner product modules
cites work: Extension theorems of continuous random linear operators on random domains
cites work: Q4489016
cites work: The James theorem in complete random normed modules
cites work: Random spectral theorems of self-adjoint random linear operators on complete complex random inner product modules
cites work: The Bishop-Phelps theorem in complete random normed modules endowed with the (\(\varepsilon, \lambda\))-topology
cites work: A further study on the Riemann-integrability for abstract-valued functions from a closed real interval to a complete random normed module
cites work: A new version of the Gleason-Kahane-Żelazko theorem in complete random normed algebras
cites work: Relations between some basic results derived from two kinds of topologies for a random locally convex module
cites work: Separation and duality in locally \(L^0\)-convex modules
cites work: Recent progress in random metric theory and its applications to conditional risk measures
cites work: Q4895670
Recommended article: On C0-semigroups of Random Linear Operators
Recommended article: Abstract random linear operators on probabilistic unitary spaces
Recommended article: Q4349545
Recommended article: On non-\(L^0\)-linear perturbations of random isometries in random normed modules
Recommended article: Probabilistic modular spaces and linear operators
Recommended article: Generalized random linear operators on a Hilbert space
Recommended article: Q3313052
Recommended article: On almost surely bounded semigroups of random linear operators
Recommended article: Random spectral theorems of self-adjoint random linear operators on complete complex random inner product modules
Recommended article: Extension theorems of continuous random linear operators on random domains
description: scientific article; zbMATH DE number 7021889