Relatively finite measure-preserving extensions and lifting multipliers by Rokhlin cocycles

Relatively Finite Measure-preserving Extensions and Lifting Multipliers by Rokhlin Cocycles

Dedicated to Stephen Smale in recognition of his contributions to topology and dynamical systems Abstract We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank mod...

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2 3 Se p 20 09 Relatively finite measure - preserving extensions and lifting multipliers by Rokhlin cocycles

Dedicated to Stephen Smale in recognition of his contributions to topology and dynamical systems Abstract We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank mod...

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ar X iv : 0 90 5 . 31 11 v 2 [ m at h . D S ] 3 1 M ay 2 00 9 Relatively finite measure - preserving extensions and lifting multipliers by Rokhlin cocycles

We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank modules associated to an extension of measure-preserving systems in the setting of a non-singular base.

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ar X iv : 0 90 5 . 31 11 v 1 [ m at h . D S ] 1 9 M ay 2 00 9 Relatively finite measure - preserving extensions and lifting multipliers by Rokhlin cocycles

We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank modules associated to an extension of measure-preserving systems in the setting of a non-singular base.

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Extensions of generic measure-preserving actions

We show that, whenever Γ is a countable abelian group and ∆ ≤ Γ is a finitely-generated subgroup, a generic measure-preserving action of ∆ on a standard atomless probability space (X,μ) extends to a free measure-preserving action of Γ on (X,μ). This extends a result of Ageev, corresponding to the case when ∆ is infinite cyclic.

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Relatively finite measure-preserving extensions and lifting multipliers by Rokhlin cocycles

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