# Tagged Questions

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### Johnson's Theorem - Proof (Runde) Clarification

I am reading Runde's Lectures on Amenability. In the proof of Johnson's theorem where he proves "$L^{1}(G)$ is amenable Banach algebra implies $G$ is amenable" : he defines a $L^1(G)$ bimodule action ...
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### Finitely presented amenable LERF group which is not virtually solvable

Is there a group $G$ with the following properties? Finitely presented Amenable Not virtually solvable LERF (that is, every finitely generated subgroup is closed in the profinite topology on $G$). ...
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### Thompson group $V$

R. Thompson introduced three groups $F\subset T\subset V$. The question concerning amenability of $F$ is still unanswered and has attracted much attention. I have read that Thompson group $V$ contains ...
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### Are finitely generated amenable groups positively finitely generated?

Let $G$ be a finitely generated amenable group. Is there a positive integer $n$ such that $n$ random elements of $G$ generate it with positive probability? Being more formal, note that $G^n$ is ...
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### Almost invariance in compact quotients of locally compact groups

While trying to get an analogue of Weiss's monotiling result for amenable residually finite groups in the topological setting, I face the following problem. Let $G$ be a locally compact amenable ...
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### Averaging measurable functions over amenable group actions

Let $G$ be an amenable group acting on a space $X$. Amenability means there is a $G$-invariant mean on $L^\infty(G,{\mathbf R})$. Given a bounded function $f\colon X\to {\mathbf R}$ one can use the ...
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### Semi-simple Banach algebra

Is there an example of an unital commutative semi-simple Banach algebra which it is not amenable?
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### Infinite topological direct sum of amenable Banach algebra

Is an infinite topological direct sum of amenable Banach algebras amenable again? Can you give me a good reference about this notion? Thanks
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### Free actions of non-amenable groups

Let $G$ be a locally compact, second countable, non-amenable group, let $X$ be a Haudorff space that is not necessarily compact, and let $G \curvearrowright X$ be a topological action that is free (i....
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### Non-ergodic Dye Theorem for orbit equivalent automorphisms

The Dye Theorem states that any two free ergodic p.m.p automorphisms of a standard probability space are orbit-equivalent. Question: Is there a version of the above theorem for non-ergodic ...
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