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

Homann, Jonathan; Kuo, Wen-Chi; Watson, Bruce

doi:10.1090/bproc/75

A Koopman-von Neumann type theorem on the convergence of Cesàro means in Riesz spaces
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by Jonathan Homann, Wen-Chi Kuo and Bruce A. Watson HTML | PDF

Proc. Amer. Math. Soc. Ser. B 8 (2021), 75-85

Abstract:

We extend the Koopman-von Neumann convergence condition on the Cesàro mean to the context of a Dedekind complete Riesz space with weak order unit. As a consequence, a characterisation of conditional weak mixing is given in the Riesz space setting. The results are applied to convergence in $L^1$.

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