When are there two-sided Folner sequences in unimodular groups?

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In Ornstein and Weiss 1987, it's shown that for unimodular amenable groups, for every compact $Ksubset G$ there exists a compact $Fsubset G$ such that $|KFK|<(1+varepsilon)|F|.$



Is there a sequential analogue of this? Like, there exists a sequence $F_n$ of compacta such that for every compact $K$, $|KF_n K|/|F_n| rightarrow 1$? If so, is it possible to start with a Folner sequence of compact sets with the property that $|KF_n|/|F_n|rightarrow 1$ and, say, pass to a subsequence that has this property?










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    In Ornstein and Weiss 1987, it's shown that for unimodular amenable groups, for every compact $Ksubset G$ there exists a compact $Fsubset G$ such that $|KFK|<(1+varepsilon)|F|.$



    Is there a sequential analogue of this? Like, there exists a sequence $F_n$ of compacta such that for every compact $K$, $|KF_n K|/|F_n| rightarrow 1$? If so, is it possible to start with a Folner sequence of compact sets with the property that $|KF_n|/|F_n|rightarrow 1$ and, say, pass to a subsequence that has this property?










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      down vote

      favorite











      In Ornstein and Weiss 1987, it's shown that for unimodular amenable groups, for every compact $Ksubset G$ there exists a compact $Fsubset G$ such that $|KFK|<(1+varepsilon)|F|.$



      Is there a sequential analogue of this? Like, there exists a sequence $F_n$ of compacta such that for every compact $K$, $|KF_n K|/|F_n| rightarrow 1$? If so, is it possible to start with a Folner sequence of compact sets with the property that $|KF_n|/|F_n|rightarrow 1$ and, say, pass to a subsequence that has this property?










      share|cite|improve this question













      In Ornstein and Weiss 1987, it's shown that for unimodular amenable groups, for every compact $Ksubset G$ there exists a compact $Fsubset G$ such that $|KFK|<(1+varepsilon)|F|.$



      Is there a sequential analogue of this? Like, there exists a sequence $F_n$ of compacta such that for every compact $K$, $|KF_n K|/|F_n| rightarrow 1$? If so, is it possible to start with a Folner sequence of compact sets with the property that $|KF_n|/|F_n|rightarrow 1$ and, say, pass to a subsequence that has this property?







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      asked Sep 1 at 5:25









      pseudocydonia

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