A multiplicative ergodic theorem for von Neumann algebra valued cocycles
Yuqing Frank Lin (Ben-Gurion University)
Thursday, March 18, 2021, 11:10 – 12:00, Online
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Oseledets’ multiplicative ergodic theorem (MET) is an important tool in smooth ergodic theory. It may be viewed as a generalization of Birkhoff’s pointwise ergodic theorem where numbers are replaced by matrices and arithmetic means are replaced by geometric means. Starting from Ruelle in 1982, many infinite-dimensional generalizations of the MET have been produced; however, these results assume quasi-compactness conditions and so do not deal with continuous spectrum. In a different direction Karlsson-Margulis obtained a geometric generalization of the MET, which we apply in our work to obtain an MET with operators in von Neumann algebras with semi-finite trace. We do not assume any compactness conditions on the operators. Joint work with Lewis Bowen and Ben Hayes.