317 research outputs found
Bergelson's Theorem for weakly mixing C*-dynamical systems
We study a nonconventional ergodic average for asymptotically abelian weakly
mixing C*-dynamical systems, related to a second iteration of Khintchine's
recurrence theorem obtained by Bergelson in the measure theoretic case. A
noncommutative recurrence theorem for such systems is obtained as a corollary.Comment: 26 page
Relatively independent joinings and subsystems of W*-dynamical systems
Relatively independent joinings of W*-dynamical systems are constructed. This
is intimately related to subsystems of W*-dynamical systems, and therefore we
also study general properties of subsystems, in particular fixed point
subsystems and compact subsystems. This allows us to obtain characterizations
of weak mixing and relative ergodicity, as well as of certain compact
subsystems, in terms of joinings.Comment: 22 page
Noncommutative recurrence over locally compact Hausdorff groups
We extend previous results on noncommutative recurrence in unital *-algebras
over the integers, to the case where one works over locally compact Hausdorff
groups. We derive a generalization of Khintchine's recurrence theorem, as well
as a form of multiple recurrence. This is done using the mean ergodic theorem
in Hilbert space, via the GNS construction.Comment: 11 page
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