Displaying similar documents to “Extreme non-Arens regularity of quotients of the Fourier algebra A(G)”

Amenability of Banach and C*-algebras on locally compact groups

A. Lau, R. Loy, G. Willis (1996)

Studia Mathematica

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Several results are given about the amenability of certain algebras defined by locally compact groups. The algebras include the C*-algebras and von Neumann algebras determined by the representation theory of the group, the Fourier algebra A(G), and various subalgebras of these.

On group representations whose C * algebra is an ideal in its von Neumann algebra

Edmond E. Granirer (1979)

Annales de l'institut Fourier

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Let τ be a continuous unitary representation of the locally compact group G on the Hilbert space H τ . Let C τ * [ V N τ ] be the C * [ W * ] algebra generated by ( L 1 ( G ) ) and M τ ( C τ * ) = φ ∈ V N τ ; φ C τ * + C τ * φ ⊂ C τ * . The main result obtained in this paper is Theorem 1: If G is σ -compact and M τ ( C τ * ) = V N τ then supp τ is discrete and each π in supp τ in CCR. We apply this theorem to the quasiregular representation τ = π H and obtain among other results that M π H ( C π H * ) = V N π H implies in many cases that G / H is a compact coset space.