Abstract
The invariant Borel probability measures play a crucial role in the study of the notion of the support of topological dynamical systems. Unfortunately, general systems with (spatial) discontinuity may not admit any invariant Borel probability measure. In this paper, we study the notion of the support of skew-product amenable semigroup action systems which may admit discontinuity. We also establish a characterization of strong proximality for these actions based on Banach proximality.
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Notes
When we say that G is a left cancellative semigroup, we mean that for any \(g, h_{1}, h_{2} \in G\), if \(gh_{1} = gh_{2}\) then \(h_{1} = h_{2}\); G is right cancellative if instead \(h_{1}g = h_{2}g\) implies \(h_{1} = h_{2}\); and G is cancellative if it is both left and right cancellative.
Throughout this paper we deal only with left Følner sequences and will routinely omit the adjective ‘left’.
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Jafari, M., Sahleh, A. & Tootkaboni, M.A. Strong Proximality for Discontinuous Skew-Product Actions of Amenable Semigroups. Mediterr. J. Math. 20, 212 (2023). https://doi.org/10.1007/s00009-023-02404-3
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DOI: https://doi.org/10.1007/s00009-023-02404-3