Displaying similar documents to “On group representations whose C * algebra is an ideal in its von Neumann algebra”

Inductive extreme non-Arens regularity of the Fourier algebra A(G)

Zhiguo Hu (2002)

Studia Mathematica

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Let G be a non-discrete locally compact group, A(G) the Fourier algebra of G, VN(G) the von Neumann algebra generated by the left regular representation of G which is identified with A(G)*, and WAP(Ĝ) the space of all weakly almost periodic functionals on A(G). We show that there exists a directed family ℋ of open subgroups of G such that: (1) for each H ∈ ℋ, A(H) is extremely non-Arens regular; (2) V N ( G ) = ⋃ H ∈ ℋ V N ( H ) and V N ( G ) / W A P ( G ̂ ) = ⋃ H ∈ ℋ [ V N ( H ) / W A P ( H ̂ ) ] ; (3) A ( G ) = ⋃ H ∈ ℋ A ( H ) and it is a WAP-strong inductive union in the sense that the unions in...

Haar measure and continuous representations of locally compact abelian groups

Jean-Christophe Tomasi (2011)

Studia Mathematica

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Let (X) be the algebra of all bounded operators on a Banach space X, and let θ: G → (X) be a strongly continuous representation of a locally compact and second countable abelian group G on X. Set σ¹(θ(g)): = λ/|λ| | λ ∈ σ(θ(g)), where σ(θ(g)) is the spectrum of θ(g), and let Σ θ be the set of all g ∈ G such that σ¹(θ(g)) does not contain any regular polygon of (by a regular polygon we mean the image under a rotation of a closed subgroup of the unit circle different from 1). We prove that...

On a variant of Kazhdan's property (T) for subgroups of semisimple groups

Mohammed Bachir Bekka, Nicolas Louvet (1997)

Annales de l'institut Fourier

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Let Γ be an irreducible lattice in a product G of simple groups. Assume that G has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of Γ in terms of the topology of the dual space G ^ of G . We use this result to give a new proof for the triviality of the first cohomology group of Γ with coefficients in a finite dimensional unitary representation.

Uniqueness of invariant product measures for elliptic infinite dimensional diffusions and particle spin systems

Alejandro F. Ramírez (2002)

ESAIM: Probability and Statistics

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Consider an infinite dimensional diffusion process process on T 𝐙 d , where T is the circle, defined by the action of its generator L on C 2 ( T 𝐙 d ) local functions as L f ( η ) = ∑ i ∈ 𝐙 d 1 2 a i ∂ 2 f ∂ η i 2 + b i ∂ f ∂ η i . Assume that the coefficients, a i and b i are smooth, bounded, finite range with uniformly bounded second order partial derivatives, that a i is only a function of η i and that inf i , η a i ( η ) > 0 . Suppose ν is an invariant product measure. Then, if ν is the Lebesgue measure or if d = 1 , 2 , it is the unique invariant measure. Furthermore, if ν is translation invariant,...

Group C*-algebras satisfying Kadison's conjecture

Rachid El Harti, Paulo R. Pinto (2011)

Banach Center Publications

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We tackle R. V. Kadison’s similarity problem (i.e. any bounded representation of any unital C*-algebra is similar to a *-representation), paying attention to the class of C*-unitarisable groups (those groups G for which the full group C*-algebra C*(G) satisfies Kadison’s problem) and thereby we establish some stability results for Kadison’s problem. Namely, we prove that A ⊗ m i n B inherits the similarity problem from those of the C*-algebras A and B, provided B is also nuclear. Then we prove...

A descriptive view of unitary group representations

Simon Thomas (2015)

Journal of the European Mathematical Society

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In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if G and H are countable amenable non-type I groups, then the unitary duals of G and H are Borel isomorphic.

Stacks of group representations

Paul Balmer (2015)

Journal of the European Mathematical Society

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We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group G , the derived and the stable categories of representations of a subgroup H can be constructed out of the corresponding category for G by a purely triangulated-categorical construction, analogous to étale extension in algebraic geometry. In the case of finite groups, we then use descent methods...

Properties of one-point completions of a noncompact metrizable space

Melvin Henriksen, Ludvík Janoš, Grant R. Woods (2005)

Commentationes Mathematicae Universitatis Carolinae

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If a metrizable space X is dense in a metrizable space Y , then Y is called a of X . If T 1 and T 2 are metric extensions of X and there is a continuous map of T 2 into T 1 keeping X pointwise fixed, we write T 1 ≤ T 2 . If X is noncompact and metrizable, then ( ℳ ( X ) , ≤ ) denotes the set of metric extensions of X , where T 1 and T 2 are identified if T 1 ≤ T 2 and T 2 ≤ T 1 , i.e., if there is a homeomorphism of T 1 onto T 2 keeping X pointwise fixed. ( ℳ ( X ) , ≤ ) is a large complicated poset studied extensively by V. Bel’nov [, Trans. Moscow Math....

Operator Segal algebras in Fourier algebras

Brian E. Forrest, Nico Spronk, Peter J. Wood (2007)

Studia Mathematica

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Let G be a locally compact group, A(G) its Fourier algebra and L¹(G) the space of Haar integrable functions on G. We study the Segal algebra S¹A(G) = A(G) ∩ L¹(G) in A(G). It admits an operator space structure which makes it a completely contractive Banach algebra. We compute the dual space of S¹A(G). We use it to show that the restriction operator u ↦ u | H : S ¹ A ( G ) → A ( H ) , for some non-open closed subgroups H, is a surjective complete quotient map. We also show that if N is a non-compact closed subgroup,...

Algebras of continuous functions over P -spaces

Nicola Rodinò (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Nella prima parte della nota sono studiate le proprietà di connessione dei sottospazi dello spettro di un anello. Con l’ausilio dei risultati ottenuti, si stabiliscono le condizioni necessarie e sufficienti affinchè un’algebra reale assolutamente piatta sia isomorfa ad un’algebra di funzioni continue a valori reali su un P -spazio, del quale determini la topologia. Ulteriori condizioni sono necessarie e sufficienti affinché un’algebra reale assolutamente piatta sia isomorfa all’algebra...

Equivalence bimodule between non-commutative tori

Sei-Qwon Oh, Chun-Gil Park (2003)

Czechoslovak Mathematical Journal

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The non-commutative torus C * ( ℤ n , ω ) is realized as the C * -algebra of sections of a locally trivial C * -algebra bundle over S ω ^ with fibres isomorphic to C * ( ℤ n / S ω , ω 1 ) for a totally skew multiplier ω 1 on ℤ n / S ω . D. Poguntke [9] proved that A ω is stably isomorphic to C ( S ω ^ ) ⊗ C * ( ℤ n / S ω , ω 1 ) ≅ C ( S ω ^ ) ⊗ A ϕ ⊗ M k l ( ℂ ) for a simple non-commutative torus A ϕ and an integer k l . It is well-known that a stable isomorphism of two separable C * -algebras is equivalent to the existence of equivalence bimodule between them. We construct an A ω - C ( S ω ^ ) ⊗ A ϕ -equivalence bimodule.

The superfocal subgroup

Marian Deaconescu (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Nel presente lavoro vengono dimostrati teoremi d'esistenza di p -complementi normali nei gruppi finiti.

Automatic continuity of operators commuting with translations

J. Alaminos, J. Extremera, A. R. Villena (2006)

Studia Mathematica

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Let τ X and τ Y be representations of a topological group G on Banach spaces X and Y, respectively. We investigate the continuity of the linear operators Φ: X → Y with the property that Φ ∘ τ X ( t ) = τ Y ( t ) ∘ Φ for each t ∈ G in terms of the invariant vectors in Y and the automatic continuity of the invariant linear functionals on X.