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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 $(L^{1} (G)) and M_{τ} (C_{τ}^{*}) = \{φ \in V N_{τ}; φ C_{τ}^{*} + C_{τ}^{*} φ \subset C_{τ}^{*}\} .$ 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 Groups of Automorphisms of the Tensor Product of von Neumann Algebras.

J. Moffat (1974)

Mathematica Scandinavica

On Inner Ideals in Ternary Algebras.

C.M. Edwards, G.T. Rüttimann (1990)

Mathematische Zeitschrift

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 Neveu decomposition and ergodic type theorems for semi-finite von Neumann algebras.

Grabarnik, G.Ya., Katz, A.A. (2003)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

On pairs of automorphisms of von Neumann algebras.

Thaheem, A.B. (1989)

International Journal of Mathematics and Mathematical Sciences

On Projection Maps of von Neumann Algebras.

Erling Stormer (1972)

Mathematica Scandinavica

On relative amenability for von Neumann algebras

Claire Anantharaman-Delaroche (1990)

Compositio Mathematica

On representation of elements of a von Neumann algebra in the form of finite sums of products of projections.

Bikchentaev, A.M. (2005)

Sibirskij Matematicheskij Zhurnal

On Some Problems of Kaplansky in the Theory of Rings of Operators.

J.D. Maitland Wright (1980)

Mathematische Zeitschrift

On some versions of Jensen's inequality on operator algebras

Ryszard Jajte (1997)

Mathematica Slovaca

On tensor porducts of von Neumann algebras.

R. Kadison, L. Ge (1996)

Inventiones mathematicae

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....

On the Conjugate Endomorphism in the Infinite Index Case.

Francesco Fidaleo, Tommaso Isola (1995)

Mathematica Scandinavica

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