5 papers
Precompactness notions in Kaplansky--Hilbert modules and extensions with discrete spectrum
Markus Haase, Henrik Kreidler
This paper is a continuation of our work on the functional-analytic core of the classical Furstenberg-Zimmer theory. We introduce and study (in the framework of lattice-ordered spa…
A Peter-Weyl theorem for compact group bundles and the geometric representation of relatively ergodic compact extensions
Nikolai Edeko, Asgar Jamneshan, Henrik Kreidler
We show that a relatively ergodic extension of measure-preserving dynamical systems has relative discrete spectrum if and only if it can be represented as a skew-product by a bundl…
A dynamical proof of the van der Corput inequality
Nikolai Edeko, Henrik Kreidler, Rainer Nagel
We provide a dynamical proof of the van der Corput inequality for sequences in Hilbert spaces that is based on the Furstenberg correspondence principle. This is done by reducing th…
A Decomposition Theorem for Unitary Group Representations on Kaplansky-Hilbert Modules and the Furstenberg-Zimmer Structure Theorem
Nikolai Edeko, Markus Haase, Henrik Kreidler
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky-Hilbert modules over Stone algebras is established, which generalizes the well-kno…
Uniform enveloping semigroupoids for groupoid actions
Nikolai Edeko, Henrik Kreidler
We establish new characterizations for (pseudo)isometric extensions of topological dynamical systems. For such extensions, we also extend results about relatively invariant measure…