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The classical multiplicative ergodic theorem (MET) for products of matrices
is a major tool in smooth ergodic theory. Since Oseledet's original proof
of the MET, various generalizations have appeared, notably to infinite
dimensional settings of products of operators on Hilbert and Banach spaces,
but these results make discreteness assumptions on the operators. Another
line of work interprets the MET geometrically, viewing each matrix as
acting isometrically on a non-positively curved space.
Without making any discreteness assumptions, we present how one of these
geometric results, of Karlsson-Margulis, can be applied to get an MET for
cocycles taking values in a finite von Neumann algebra.
This is joint work with Lewis Bowen and Ben Hayes.
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