TY - EJOUR
AB - The special linear group G = SLn(Z[x(1), ... , x(k)]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, and p be any real number in (1, infinity). The main result is the following: any finite index subgroup of G has the fixed point property with respect to every affine isometric action on the space of p-Schatten class operators. It is in addition shown that higher rank lattices have the same property. These results are a generalization of previous theorems respectively of the author and of Bader-Furman-Gelander-Monod, which treated a commutative L-p-setting.
T1 - Fixed Point Property For Universal Lattice On Schatten Classes
IS - 1
DA - 2013
AU - Mimura, Masato
JF - Proceedings Of The American Mathematical Society
SP - 65-81
VL - 141
EP - 65-81
PB - Amer Mathematical Soc
PP - Providence
ID - 190915
KW - Fixed point property
KW - Kazhdan's property (T)
KW - Schatten class operators
KW - noncommutative L-p-spaces
KW - bounded cohomology
SN - 0002-9939
ER -