کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6415033 | 1334901 | 2016 | 42 صفحه PDF | دانلود رایگان |
We characterize those locally compact, second countable, amenable groups in which a density version of Hindman's theorem holds and those countable, amenable groups in which a two-sided density version of Hindman's theorem holds. In both cases the possible failure can be attributed to an abundance of finite-dimensional unitary representations, which allows us to construct sets with large density that do not contain any shift of a set of measurable recurrence, let alone a shift of a finite products set. The possible success is connected to the ergodic-theoretic phenomenon of weak mixing via a two-sided version of the Furstenberg correspondence principle.We also construct subsets with large density that are not piecewise syndetic in arbitrary non-compact amenable groups. For countably infinite amenable groups, the symbolic systems associated to such sets admit invariant probability measures that are not concentrated on their minimal subsystems.
Journal: Journal of Functional Analysis - Volume 270, Issue 6, 15 March 2016, Pages 2126-2167