A Koopman-von Neumann type theorem on the convergence of Cesàro means in Riesz spaces

DOI10.1090/bproc/75OpenAlexW3132709318MaRDI QIDQ5855737

Jonathan Homann, Wen-Chi Kuo, Bruce Alastair Watson

Publication date: 19 March 2021

Published in: Proceedings of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.12215

zbMATH Keywords

weak mixingCesàro meanRiesz spacesorder convergenceconditional expectation operatorsKoopman-von Neumann condition

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Ergodic theory of linear operators (47A35) Ergodicity, mixing, rates of mixing (37A25) Ordered topological linear spaces, vector lattices (46A40)

Related Items (3)

The Kac formula and Poincaré recurrence theorem in Riesz spaces ⋮ Characterisation of conditional weak mixing via ergodicity of the tensor product in Riesz spaces ⋮ Ergodicity in Riesz Spaces

Cites Work

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• \(L^p\)-spaces with respect to conditional expectation on Riesz spaces
• An Andô-Douglas type theorem in Riesz spaces with a conditional expectation
• Ergodic theory and the strong law of large numbers on Riesz spaces
• Ergodic theorems. With a supplement by Antoine Brunel
• Banach lattices
• Mixing inequalities in Riesz spaces
• Conditional expectations on Riesz spaces
• Mixingales on Riesz spaces
• Jensen's and martingale inequalities in Riesz spaces
• The Hájek-Rényi-Chow maximal inequality and a strong law of large numbers in Riesz spaces
• Uo-convergence and its applications to Cesàro means in Banach lattices
• Limit laws for martingales in vector lattices
• Operator Theoretic Aspects of Ergodic Theory

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