On a decomposition of a von Neumann algebra
Let be a continuous unitary representation of the locally compact group on the Hilbert space . Let be the algebra generated byThe main result obtained in this paper is Theorem 1:If is -compact and then supp is discrete and each in supp in CCR.We apply this theorem to the quasiregular representation and obtain among other results that implies in many cases that is a compact coset space.
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.
The notion of bundle convergence in von Neumann algebras and their -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....