**SEMINARIO TEORIA DE GRUPOS UAM-ICMAT **

**Adrián González Pérez (KU Leuven) **

*Notions of amenability and asymptotic $L_p$-Isometries *

**Martes, 30. Mayo 2017 **

** Sala 520: 14:30-15:30 **

__Abstract__**: Given a nonabelian group $G$ it is possible to express certain approximation properties ---like amenability, weak amenability or the Haagerup property--- as existence of families of Fourier multipliers approximating the identity. The same characterization survives after replacing Fourier multipliers by the so called Herz-Schur multipliers. Similar approximation properties can be defined in the corresponding noncommutative $L_p$ space, where they yield weaker approximation properties. In the ``weaker'' $L_p$-context both the equivalence of approximation-by-Fourier and approximation-by-Schur multipliers and the equivalence of the approximation property for $G$ and for a lattice $Gamma leq G$ are unknown. Nevertheless intertwining techniques that use some form of amenability can be used to translate between the two. We will discuss such intertwining results as well as the necessity of the conditions involved. **