000190915 001__ 190915
000190915 005__ 20180913062154.0
000190915 022__ $$a0002-9939
000190915 02470 $$2ISI$$a000326513700006
000190915 037__ $$aARTICLE
000190915 245__ $$aFixed Point Property For Universal Lattice On Schatten Classes
000190915 260__ $$aProvidence$$bAmer Mathematical Soc$$c2013
000190915 269__ $$a2013
000190915 300__ $$a17
000190915 336__ $$aJournal Articles
000190915 520__ $$aThe 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.
000190915 6531_ $$aFixed point property
000190915 6531_ $$aKazhdan's property (T)
000190915 6531_ $$aSchatten class operators
000190915 6531_ $$anoncommutative L-p-spaces
000190915 6531_ $$abounded cohomology
000190915 700__ $$aMimura, Masato$$uUniv Tokyo, Grad Sch Math Sci, Komaba, Tokyo 1538914, Japan
000190915 773__ $$j141$$k1$$q65-81$$tProceedings Of The American Mathematical Society
000190915 909C0 $$0252235$$pEGG$$xU11822
000190915 909CO $$ooai:infoscience.tind.io:190915$$pSB$$particle
000190915 917Z8 $$x181579
000190915 937__ $$aEPFL-ARTICLE-190915
000190915 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000190915 980__ $$aARTICLE