Abstract
Let \(\mathbf{E}=\mathbf{E}(\Omega,\mathcal{F},\mu)\) be a symmetric Banach space of measurable functions on a measure space \((\Omega,\mathcal{F},\mu)\). We prove a version of Mean (Statistical) Ergodic Theorem for Cesáro averages \(A_{n,T}f=1/n\sum_{k=1}^{n}T^{k-1}f\), \(f\in\mathbf{E}\), while operators on \(\mathbf{E}\) are induced by positive absolute contraction in \(\mathbf{L}_{1}+\mathbf{L}_{\infty}=(\mathbf{L}_{1}+\mathbf{L}_{\infty})(\Omega,\mathcal{F},\mu)\).
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Muratov, M., Pashkova, Y. & Rubshtein, BZ. Mean Ergodic Theorems in Symmetric Spaces of Measurable Functions. Lobachevskii J Math 42, 949–966 (2021). https://doi.org/10.1134/S1995080221050103
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DOI: https://doi.org/10.1134/S1995080221050103