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Journal of Operator Theory

Volume 86, Issue 2, Fall 2021  pp. 469-501.

Ergodic properties of convolution operators

Authors:  Jorge Galindo (1), Enrique Jorda (2)
Author institution:(1) Instituto Universitario de Matematicas y Aplicaciones (IMAC), Universidad Jaume I, E-12071, Castellon, Spain
(2) Instituto Universitario de Matematica Pura y Aplicada IUMPA, Universitat Politecnica de Valencia, Plaza Ferrandiz y Carbonell s/n E-03801 Alcoy, Spain

Summary: Let $G$ be a locally compact group and $\mu$ be a measure on $G$. In this paper we find conditions for the convolution operators $\lambda_p(\mu): L^p(G)\to L^p(G)$ to be mean ergodic and uniformly mean ergodic. The ergodic properties of the operators $\lambda_p(\mu)$ are related to the ergodic properties of the measure $\mu$ as well.

Keywords: mean ergodic operator, uniformly mean ergodic operator, convolution operator, locally compact group, amenable group

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