On mean ergodic semigroups of random linear operators

DOI10.3792/PJAA.88.53zbMath1250.47007OpenAlexW2165329706MaRDI QIDQ431733

Xia Zhang

Publication date: 30 June 2012

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pja/1333631993

zbMATH Keywords

random normed moduleergodic semigroup of random linear operatorsrandom reflexivity

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Groups and semigroups of linear operators (47D03) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Reflexivity and semi-reflexivity (46A25)

Related Items (7)

A characterization for a complete random normed module to be mean ergodic ⋮ On conditional mean ergodic semigroups of random linear operators ⋮ Unnamed Item ⋮ An exponential representation for random C₀–semigroups ⋮ \(L^0\)-linear modulus of a random linear operator ⋮ On almost surely bounded semigroups of random linear operators ⋮ On non-\(L^0\)-linear perturbations of random isometries in 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
• Von Neumann's mean ergodic theorem on complete random inner product modules
• Relations between some basic results derived from two kinds of topologies for a random locally convex module
• Random strict convexity and random uniform convexity in random normed modules
• 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
• One-Parameter Semigroups for Linear Evolution Equations
• Convergence of elements in random normed spaces
• On Almost Sure Convergence in Linear Spaces of Random Variables
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