Related papers: A property (T) for C*-algebras

We introduce stabilised property Gamma, a C*-algebraic variant of property Gamma which is invariant under stable isomorphism. We then show that simple separable nuclear C*-algebras with stabilised property Gamma and $\mathrm{Cu}(A) \cong…

We develop a new method, based on non-vanishing of second cohomology groups, for proving the failure of lifting properties for full C$^*$-algebras of countable groups with (relative) property (T). We derive that the full C$^*$-algebras of…

If $\alpha$ is an amenable action of a discrete group $G$ on a unital C*-algebra $A$, then the crossed-product C*-algebra $A\rtimes_\alpha G$ has the weak expectation property if and only if $A$ has this property.

For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property,…

For $n\geq 3,$ let $\Gamma=SL_n(\mathbb Z).$ We prove the following superridigity result for $\Gamma$ in the context of operator algebras. Let $L(\Gamma)$ be the von Neumann algebra generated by the left regular representation of $\Gamma.$…

We investigate Matui-Sato's notion of property (SI) for C*-dynamics, this time with a focus on actions of possibly non-amenable groups. The main result is a generalization of earlier work: For any countable group $\Gamma$ and any…

We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C*-algebra has a…

Let $\Gamma$ be a countable group and $(X, \Gamma)$ a compact topological dynamical system. We study the question of the existence of an intermediate $C^*$-subalgebra $\mathcal{A}$ $$C^{*}_{r}(\Gamma)<\mathcal{A}<C(X)\rtimes_r\Gamma,$$…

In this paper, we consider $\text{C}^*$-algebras with the ideal property (the ideal property unifies the simple and real rank zero cases). We define two categories related the invariants of the $\text{C}^*$-algebras with the ideal property.…

We study bounded bilinear maps on a C$^*$-algebra $A$ having product property at $c\in A$. This leads us to the question of when a C$^*$-algebra is determined by products at $c.$ In the first part of our paper, we investigate this question…

For an action of a discrete group $\Gamma$ on a set $X$, we show that the Schreier graph on $X$ has property A if and only if the permutation representation on $\ell_2X$ generates an exact $\mathrm{C}^*$-algebra. This is well known in the…

For II$_1$ factors, we show that property (T) is equivalent to weak spectral gap in any inclusion into a larger tracial von Neumann algebra. We also show that not having non-zero almost central vectors in weakly mixing bimodules…

We show by construction that when $G$ is an elementary amenable group and $A$ is a unital simple nuclear and tracially approximately divisible $C^*$-algebra, there exists an action $\omega$ of $G$ on $A$ with the tracial Rokhlin property in…

In his study of the relative Dixmier property for inclusions of von Neumann algebras and of $C^*$-algebras, Popa considered a certain property of automorphisms on $C^*$-algebras, that we here call the strong averaging property. In this note…

We prove that, for a free action $\alpha \colon G \curvearrowright X$ of a countably infinite discrete amenable group on a compact metric space, the small boundary property is implied by uniform property $\Gamma$ of the Cartan subalgebra…

We study Property (T) in the $\Gamma(n,k,d)$ model of random groups: as $k$ tends to infinity this gives the Gromov density model, introduced in [Gro93]. We provide bounds for Property (T) in the $k$-angular model of random groups, i.e. the…

We prove that for every exact discrete group $\Gamma$, there is an intermediate C*-algebra between the reduced group C*-algebra and the intersection of the group von Neumann algebra and the uniform Roe algebra which is realized as the…

We say that a C*-algebra is soft if it has no nonzero unital quotients, and we connect this property to the Hjelmborg-R{\o}rdam condition for stability and to property (S) of Ortega-Perera-R{\o}rdam. We further say that an operator in a…

We show that Property $\mathrm{(TTT)}$ is an obstruction to weak amenability with Cowling--Haagerup constant $1$. More precisely, if $G$ is a countable group and $H$ is an infinite subgroup of $G$ such that the pair $(G,H)$ has relative…

Property (T) for groups means a dichotomy: a representation either has an invariant vector or all vectors are far from being invariant. We show that, under a stronger condition of A.Zuk, a similar dichotomy holds for almost representations…