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?
amenability
add a comment |Â
up vote
0
down vote
favorite
up vote
0
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?
amenability
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?
amenability
amenability
asked Sep 1 at 5:25
pseudocydonia
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