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		   Technion - Israel Institute of Technology
			   Department of Mathematics
 
                                ===============
                                SPECIAL SEMINAR
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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
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Uri Bader   <uri.bader@gmail.com>