相关论文: On Ozawa's Property for Free Group Factors

We prove a converse to Myhill's "Garden-of-Eden" theorem and obtain in this manner a characterization of amenability in terms of cellular automata: "A group $G$ is amenable if and only if every cellular automaton with carrier $G$ that has…

For a locally compact Abelian group $G$ and a continuous weight function $\omega$ on $G$ we show that the Beurling algebra $L^1(G, \omega)$ is weakly amenable if and only if there is no nontrivial continuous group homomorphism $\phi$: $G\to…

Suppose $(X,\sigma)$ is a subshift, $P_X(n)$ is the word complexity function of $X$, and ${\rm Aut}(X)$ is the group of automorphisms of $X$. We show that if $P_X(n)=o(n^2/\log^2 n)$, then ${\rm Aut}(X)$ is amenable (as a countable,…

Applying Popa's orthogonality method to a new class of groups, we construct amenable group factors which are prime and have no infinite dimensional regular abelian *-subalgebras. By adjusting Farah--Katsura's solution of Dixmier's problem…

Given a topologically free action of a countably infinite amenable group on the Cantor set, we prove that, for every subgroup $G$ of the topological full group containing the alternating group, the group von Neumann algebra $\mathscr{L} G$…

We prove that for every automata algebra of exponential growth, the associated Lie algebra contains a free subalgebra. For n\geq 1, let L_{n+2} be a Lie algebra with generator set x_1,..., x_{n+2} and the following relations: for k\leq n,…

We prove that for any free ergodic probability measure preserving action \F_n \actson (X,\mu) of a free group on n generators \F_n, 2 \leq n \leq \infty, the associated group measure space II_1 factor $L^\infty(X) \rtimes \F_n$ has…

We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen `exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the permutation group) to…

We study class $\mathcal S$ for locally compact groups. We characterize locally compact groups in this class as groups having an amenable action on a boundary that is small at infinity, generalizing a theorem of Ozawa. Using this…

Let M be a tracial von Neumann algebra and A be a weakly dense unital C*-subalgebra of M. We say that a set X is a W*-generating set for M if the von Neumann algebra generated by X is M and that X is a C*-generating set for A if the unital…

Using Voiculsecu's free entropy, it is shown that the free group factors L(F_n) lack property C of Popa and that they lack finite multiplicity abelian subalgebras. Property C is an assymptotic commutivity property.

Let $M$ be a II$_1$ factor with a von Neumann subalgebra $Q\subset M$ that has infinite index under any projection in $Q'\cap M$ (e.g., $Q$ abelian; or $Q$ an irreducible subfactor with infinite Jones index). We prove that given any…

In this short note, further to Ng's study, we extend Bekka amenability and weak Bekka amenability to general locally compact quantum groups. We generalize some Ng's results to the general case. In particular, we show that, a locally compact…

We refine a construction of Choi, Farah and Ozawa to build a nonseparable amenable operator algebra $\mathcal A\subseteq\ell_\infty(M_2)$ whose nonseparable subalgebras, including $\mathcal A$, are not isomorphic to a $C^*$-algebra. This is…

The recent breakthrough works [6,8,9] which established the amenability for new classes of groups, lead to the following question: is the action $W(\mathbb{Z}^d) \curvearrowright \mathbb{Z}^d$ extensively amenable? (Where $W(\mathbb{Z}^d)$…

Let $f_1, f_2, ..., f_n$ be a family of independent copies of a given random variable f in a probability space $(\Omega, \mathcal{F}, \mu)$. Then, the following equivalence of norms holds whenever $1 \le q \le p < \infty$…

We show that a large class of i.c.c., countable, discrete groups satisfying a weak negative curvature condition are not inner amenable. By recent work of Hull and Osin, our result recovers that mapping class groups and Out(F_n) are not…

Let $R=K[G]$ be a group ring of a group $G$ over a field $K$. It is known that if $G$ is amenable then $R$ satisfies the Ore condition: for any $a,b\in R$ there exist $u,v\in R$ such that $au=bv$, where $u\ne0$ or $v\ne0$. It is also true…

The original definition of amenability given by von Neumann in the highly non-constructive terms of means was later recast by Day using approximately invariant probability measures. Moreover, as it was conjectured by Furstenberg and proved…

We show that if $\Gamma\curvearrowright (X^\Gamma,\mu^\Gamma)$ is a Bernoulli action of an i.c.c. nonamenable group $\Gamma$ which is weakly amenable with Cowling-Haagerup constant $1$, and $\Lambda\curvearrowright(Y,\nu)$ is a free ergodic…