Is every action from an amenable group amenable on a unital \$C^*\$-algebra? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T02:29:01Z http://mathoverflow.net/feeds/question/42322 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/42322/is-every-action-from-an-amenable-group-amenable-on-a-unital-c-algebra Is every action from an amenable group amenable on a unital \$C^*\$-algebra? m07kl 2010-10-15T20:01:29Z 2010-10-16T06:37:28Z <p>Is every action from an amenable group amenable on a unital \$C^*\$-algebra?</p> http://mathoverflow.net/questions/42322/is-every-action-from-an-amenable-group-amenable-on-a-unital-c-algebra/42367#42367 Answer by Makoto Yamashita for Is every action from an amenable group amenable on a unital \$C^*\$-algebra? Makoto Yamashita 2010-10-16T06:37:28Z 2010-10-16T06:37:28Z <p>Yes it is. It follows from Theorem 3.3 of [1] and the fact that the trivial action of an amenable group on \$\mathbb{C}\$ is amenable. More modern reference is [2] (in particular Section 4.3).</p> <p>[1] C. Anantharaman-Delaroche. Systèmes dynamiques non commutatifs et moyennabilité. Math. Ann., 279(2):297–315, 1987.</p> <p>[2] N. P. Brown and N. Ozawa. C*-algebras and finite-dimensional approximations, volume 88 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2008.</p>