Related papers: Simple Lie groups without the Approximation Proper…

We prove that the universal covering group $\widetilde{\mathrm{Sp}}(2,\mathbb{R})$ of $\mathrm{Sp}(2,\mathbb{R})$ does not have the Approximation Property (AP). Together with the fact that $\mathrm{SL}(3,\mathbb{R})$ does not have the AP,…

We give a complete characterization of connected Lie groups with the Approximation Property for groups (AP). To this end, we introduce a strengthening of property (T), that we call property (T*), which is a natural obstruction to the AP. In…

We prove that, for any $1<p<\infty$, the groups $\text{SL}(3,\mathbb{R})$ and $\text{Sp}(2,\mathbb{R})$ do not have the $p\,$-approximation property of An, Lee and Ruan, which implies in particular that they are not $p\,$-weakly amenable.…

In 2010, Lafforgue and de la Salle gave examples of noncommutative Lp-spaces without the operator space approximation property (OAP) and, hence, without the completely bounded approximation property (CBAP). To this purpose, they introduced…

It is proved that: (1) The Fourier algebra A(G) of a simple Lie group G of real rank at least 2 with finite center does not have a multiplier bounded approximate unit. (2) The reduced C*-algebra of any lattice in a non-compact simple Lie…

Let $G$ be the symplectic group $Sp_4$ over a non Archimedean local field of any characteristic. It is proved in this paper that for $p\in[1,4/3)\cup (4,\infty]$ neither the group $G$ nor its lattices have the property of approximation by…

In this paper we consider the class of connected simple Lie groups equipped with the discrete topology. We show that within this class of groups the following approximation properties are equivalent: (1) the Haagerup property; (2) weak…

In this work, we study groupoids and their approximation properties, generalizing both the definitions and some known results for the group case. More precisely, we introduce weak amenability for groupoids using the definition of the…

We extend a theorem of Haagerup and Kraus in the C*-algebra context: for a locally compact group with the approximation property (AP), the reduced C*-crossed product construction preserves the strong operator approximation property (SOAP).…

Let $1 < p < \infty$. It is shown that if $G$ is a discrete group with the approximation property introduced by Haagerup and Kraus, then the non-commutative $L_p(VN(G))$ space has the operator space approximation property. If, in addition,…

Recently, a complete characterization of connected Lie groups with the Approximation Property was given. The proof used of the newly introduced property (T*). We present here a short proof of the same result avoiding the use of property…

We prove that a locally compact group has the approximation property (AP), introduced by Haagerup-Kraus, if and only if a non-commutative Fej\'{e}r theorem holds for the associated $C^*$- or von Neumann crossed products. As applications, we…

For any 1\leq p \leq \infty different from 2, we give examples of non-commutative Lp spaces without the completely bounded approximation property. Let F be a non-archimedian local field. If p>4 or p<4/3 and r\geq 3 these examples are the…

For a locally compact group $G$, let $A^n(G)$ denote the multidimensional Fourier algebra given by $ \otimes_{n}^{eh} A(G).$ This work explores the approximation identity and operator amenability of the algebra $A^n(G)$. Further, we study…

We show that for a locally compact group $G$, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra $A(G)$ satisfies a completely bounded version Pisier's similarity property with…

We prove that if $G$ is a discrete group and $(A,G,\alpha)$ is a C*-dynamical system such that the reduced crossed product $A\rtimes_{r,\alpha} G$ possesses property (SOAP) then every completely compact Herz-Schur $(A,G,\alpha)$-multiplier…

We prove that connected higher rank simple Lie groups have Lafforgue's strong property (T) with respect to a certain class of Banach spaces $\mathcal{E}_{10}$ containing many classical superreflexive spaces and some non-reflexive spaces as…

We define for discrete finitely presented groups a new property related to their asymptotic representations. Namely we say that a groups has the property AGA if every almost representation generates an asymptotic representation. We give…

A locally compact group $ G $ is discrete if and only if the Fourier algebra $ A(G) $ has a non-zero (weakly) compact multiplier. We partially extend this result to the setting of ultraspherical hypergroups. Let $H$ be an ultraspherical…

Let $G$ be a locally compact group. If $G$ is finite then the amenability constant of its Fourier algebra, denoted by ${\rm AM}({\rm A}(G))$, admits an explicit formula [Johnson, JLMS 1994]; if $G$ is infinite then no such formula for ${\rm…