Displaying similar documents to “Hilbert C*-modules from group actions: beyond the finite orbits case”

Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras

Maria Joiţa (2009)

Open Mathematics

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We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C *-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E *(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E *) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc....

Hilbert C*-modules and amenable actions

Ronald G. Douglas, Piotr W. Nowak (2010)

Studia Mathematica

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We study actions of discrete groups on Hilbert C*-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant.

On full Hilbert C * -modules.

Moslehian, Mohammad Sal (2001)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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A Morita equivalence for Hilbert C*-modules

Maria Joiţa, Mohammad Sal Moslehian (2012)

Studia Mathematica

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We introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate the properties of the new Morita equivalence. We apply our results to study continuous actions of locally compact groups on full Hilbert C*-modules. We also present an extension of Green's theorem in the context of Hilbert C*-modules.

Homogenization of codimension 1 actions of ℝ n near a compact orbit

Marcos Craizer (1994)

Annales de l'institut Fourier

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Let Φ be a C ∞ ℝ n -action on an orientable ( n + 1 ) -dimensional manifold. Assume Φ has an isolated compact orbit T and let W be a small tubular neighborhood of it. By a C ∞ change of variables, we can write W = ℝ n / ℤ n × I and T = 𝕋 n × [ 0 ] , where I is some interval containing 0. In this work, we show that by a C 0 change of variables, C ∞ outside T , we can make Φ | W invariant by transformations of the type ( x , z ) → ( x + a , z ) , a ∈ ℝ n , where x ∈ ℝ n / ℤ n and z ∈ I . As a corollary one cas describe completely the dynamics of Φ in W .

Topological classification of multiaxial U ( n ) -actions (with an appendix by Jared Bass)

Sylvain Cappell, Shmuel Weinberger, Min Yan (2015)

Journal of the European Mathematical Society

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This paper begins the classification of topological actions on manifolds by compact, connected, Lie groups beyond the circle group. It treats multiaxial topological actions of unitary and symplectic groups without the dimension restrictions used in earlier works by M. Davis and W. C. Hsiang on differentiable actions. The general results are applied to give detailed calculations for topological actions homotopically modeled on standard multiaxial representation spheres. In the present...

How restrictive is topological dynamics?

Anzelm Iwanik (1997)

Commentationes Mathematicae Universitatis Carolinae

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Let T be a permutation of an abstract set X . In ZFC, we find a necessary and sufficient condition it terms of cardinalities of the T -orbits that allows us to topologize ( X , T ) as a topological dynamical system on a compact Hausdorff space. This extends an early result of H. de Vries concerning compact metric dynamical systems. An analogous result is obtained for 𝐙 2 -actions without periodic points.

Topological friction in aperiodic minimal ℝ m -actions

Jarosław Kwapisz (2010)

Fundamenta Mathematicae

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For a continuous map f preserving orbits of an aperiodic ℝ m -action on a compact space, its displacement function assigns to x the “time” t ∈ ℝ m it takes to move x to f(x). We show that this function is continuous if the action is minimal. In particular, f is homotopic to the identity along the orbits of the action.

Normal Hilbert modules over the ball algebra A(B)

Kunyu Guo (1999)

Studia Mathematica

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The normal cohomology functor E x t ℵ is introduced from the category of all normal Hilbert modules over the ball algebra to the category of A(B)-modules. From the calculation of E x t ℵ -groups, we show that every normal C(∂B)-extension of a normal Hilbert module (viewed as a Hilbert module over A(B) is normal projective and normal injective. It follows that there is a natural isomorphism between Hom of normal Shilov modules and that of their quotient modules, which is a new lifting theorem of normal...

Shadowing in multi-dimensional shift spaces

Piotr Oprocha (2008)

Colloquium Mathematicae

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We show that the class of expansive ℤ d actions with P.O.T.P. is wider than the class of actions topologically hyperbolic in some direction ν ∈ ℤ d . Our main tool is an extension of a result by Walters to the multi-dimensional symbolic dynamics case.