Displaying similar documents to “Non-abelian extensions have nonsimple spectrum”

On the multiplicity function of ergodic group extensions of rotations

G. Goodson, J. Kwiatkowski, M. Lemańczyk, P. Liardet (1992)

Studia Mathematica

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For an arbitrary set A ⊆ ℕ satisfying 1 ∈ A and lcm(m₁,m₂) ∈ A whenever m₁,m₂ ∈ A, an ergodic abelian group extension of a rotation for which the range of the multiplicity function equals A is constructed.

Cyclic space isomorphism of unitary operators

Krzysztof Frączek (1997)

Studia Mathematica

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We introduce a new equivalence relation between unitary operators on separable Hilbert spaces and discuss a possibility to have in each equivalence class a measure-preserving transformation.

Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations

Chris Dodd, Phakawa Jeasakul, Anne Jirapattanakul, Daniel M. Kane, Becky Robinson, Noah D. Stein, Cesar E. Silva (2010)

Colloquium Mathematicae

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We define a class of discrete Abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply recurrent. We then study conditions sufficient for showing that Cartesian products of transformations are conservative for a class of invertible infinite measure-preserving transformations and provide examples of these transformations.

A spectral theory for locally compact abelian groups of automorphisms of commutative Banach algebras

Sen Huang (1999)

Studia Mathematica

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Let A be a commutative Banach algebra with Gelfand space ∆ (A). Denote by Aut (A) the group of all continuous automorphisms of A. Consider a σ(A,∆(A))-continuous group representation α:G → Aut(A) of a locally compact abelian group G by automorphisms of A. For each a ∈ A and φ ∈ ∆(A), the function φ a ( t ) : = φ ( α t a ) t ∈ G is in the space C(G) of all continuous and bounded functions on G. The weak-star spectrum σ w * ( φ a ) is defined as a closed subset of the dual group Ĝ of G. For φ ∈ ∆(A) we define Ʌ φ a to be the...