Comments on: Some notes on amenability
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoSun, 17 Jan 2021 21:16:28 +0000
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By: DHan
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-618466
Sun, 17 Jan 2021 21:16:28 +0000http://terrytao.wordpress.com/?p=2059#comment-618466I think in theorem 1, the part from (ii) to (iii), the first inequality is not very clear from the observation. I prefer Namioka’s proof for this. But anyway, many thanks for this post!
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By: Generalisations of the limit functional | What's new
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-480545
Thu, 11 May 2017 23:25:10 +0000http://terrytao.wordpress.com/?p=2059#comment-480545[…] can be viewed as a demonstration of the amenability of the natural numbers (or integers); see this previous blog post for further […]
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By: S.
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-472514
Fri, 23 Sep 2016 10:15:55 +0000http://terrytao.wordpress.com/?p=2059#comment-472514Nice. I have a question about the conditions (iii) and (iv) in Theorem 1:, is there a possibility to prove the equivalence of both conditions without using that is countable?
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By: Mustafa Said
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-218979
Sat, 09 Mar 2013 08:19:53 +0000http://terrytao.wordpress.com/?p=2059#comment-218979There is a good set of notes on “Amenability for von Neumann Algebras, Hyperfiniteness” by Remi Boutonnet
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By: First Bourbaki seminar of 2013 « Disquisitiones Mathematicae
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-214252
Wed, 23 Jan 2013 10:49:36 +0000http://terrytao.wordpress.com/?p=2059#comment-214252[…] For more details on these properties (in the case of countable groups), the reader might want to consult Terence Tao’s notes on this subject. […]
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By: dasziggy
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-151906
Fri, 13 Jul 2012 18:22:40 +0000http://terrytao.wordpress.com/?p=2059#comment-151906In Theorem 1, (i) ==> (ii), shouldn’t the negation of (ii) be:

“There exists {S, \epsilon} s.t. for all means {\nu} there \textbf{exists} {x \in S} such that {\| \nu – \tau_x \nu\|_{\ell^1(G)} > \epsilon} .”

[Corrected, thanks – T.]

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By: Robert Treger
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-120012
Mon, 02 Jan 2012 11:29:39 +0000http://terrytao.wordpress.com/?p=2059#comment-120012Consider a projective manifold X with large, residually finite, and a non-amenable fundamental group. Let U denote its universal covering. It is known that U has infinitely many bounded harmonic functions. Do those functions separate points on U provided U is Stein?
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By: A computational perspective on set theory « What’s new
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-43937
Sat, 20 Mar 2010 05:54:05 +0000http://terrytao.wordpress.com/?p=2059#comment-43937[…] low and high dimensional cases is that the free group is not amenable, whereas is amenable. See these previous blog posts for further discussion.) Possibly related posts: (automatically generated)The “no […]
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By: Some notes on group extensions « What’s new
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-43337
Sat, 23 Jan 2010 08:15:30 +0000http://terrytao.wordpress.com/?p=2059#comment-43337[…] results in group theory in a succinct form using this notation. For instance, one of the results in my earlier blog post on amenability now states that amenable-by-amenable groups are amenable. Another example that I have been looking […]
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By: excuses, excuses « Since it is not …
https://terrytao.wordpress.com/2009/04/14/some-notes-on-amenability/#comment-41113
Sun, 23 Aug 2009 05:06:45 +0000http://terrytao.wordpress.com/?p=2059#comment-41113[…] sometimes it allows quicker/slicker proofs of certain results (for instance, see Prop. 5 in these expository notes by Terence Tao). So, I thought it might be worth a post looking at amenability from the function-space […]
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