------------------------------------------------------------------------------- Technion - Israel Institute of Technology Department of Mathematics =============== SPECIAL SEMINAR =============== SPEAKER: Tsachik Gelander TITLE: Fun with L^1 DATE: Thursday, 16 December, 2010 PLACE: Amado, 9th floor TIME: 16:30 ABSTRACT: Jointly with U. Bader and N. Monod we proved the following fixed point theorem for L_1 spaces: Theorem: Let A be a non-empty bounded subset of an L_1 space V. Then there is a point in V fixed by every isometry of V preserving A. Although our proof is fairly simple, the theorem has many immediate applications, for instance: Corollary 1: For every locally compact group G, any derivation D:L^1(G)-->L^1(G) is inner. This is the famous "derivation problem" which was intensively studied since the 1960's and was solved in 2008 by V. Losert. Corollary 2: Every C*-algebra is weakly amenable. This was first proved by U. Haagerup using the Grothendieck-Haagerup-Pisier inequality. Another surprising application is the following new characterization of property (T): Corollary 3: A lcsc group G has property (T) iff every isometric action of G on L_1[0,1] has a fixed point. For further information please contact: Uri Bader <uri.bader@gmail.com> Phone: 4174 --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Uri Bader <uri.bader@gmail.com>