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

Edmond E. Granirer (1979)

Annales de l'institut Fourier

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.

On local derivations in the Kadison sense

Andrzej Nowicki (2001)

Colloquium Mathematicae

Let k be a field. We prove that any polynomial ring over k is a Kadison algebra if and only if k is infinite. Moreover, we present some new examples of Kadison algebras and examples of algebras which are not Kadison algebras.

On the bundle convergence of double orthogonal series in noncommutative L 2 -spaces

Ferenc Móricz, Barthélemy Le Gac (2000)

Studia Mathematica

The notion of bundle convergence in von Neumann algebras and their L 2 -spaces for single (ordinary) sequences was introduced by Hensz, Jajte, and Paszkiewicz in 1996. Bundle convergence is stronger than almost sure convergence in von Neumann algebras. Our main result is the extension of the two-parameter Rademacher-Men’shov theorem from the classical commutative case to the noncommutative case. To our best knowledge, this is the first attempt to adopt the notion of bundle convergence to multiple series....

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