Fixed Point Property For Universal Lattice On Schatten Classes

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.


Published in:
Proceedings Of The American Mathematical Society, 141, 1, 65-81
Year:
2013
Publisher:
Providence, Amer Mathematical Soc
ISSN:
0002-9939
Keywords:
Laboratories:




 Record created 2013-12-09, last modified 2018-09-13


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