Mimura, Masato2013-12-092013-12-092013-12-09201310.1090/S0002-9939-2012-11711-3https://infoscience.epfl.ch/handle/20.500.14299/97529WOS:000326513700006The 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.Fixed point propertyKazhdan's property (T)Schatten class operatorsnoncommutative L-p-spacesbounded cohomologytext::journal::journal article::research article