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$C^{*}$ algebras associated with von Neumann algebras

Tullio G. Ceccherini-Silberstein (1999)

Bollettino dell'Unione Matematica Italiana

Ad un'algebra di von Neumann separabile $M$ , in forma standard su di uno spazio di Hilbert $H$ , si associa la $C^{*}$ algebra $O_{M}$ definita come la $C^{*}$ algebra $O_{U (M)}$ costituita dai punti fissi dell'algebra di Cuntz generalizzata $O_{H}$ mediante l'azione canonica del gruppo $U (M)$ degli unitari di $M$ . Si dà una caratterizzazione di $O_{M}$ nel caso in cui $M$ è un fattore iniettivo. In seguito, come applicazione della teoria dei sistemi asintoticamente abeliani, si mostra che, se $ω$ è uno stato vettoriale normale e fedele di $M$ , la restrizione...

Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann

Alain Connes (1974)

Annales de l'institut Fourier

Nous démontrons que la catégorie de von Neumann est équivalente à la catégorie des cônes autopolaires, facialement homogènes, complexes. Un cône $\lor$ dans un espace hilbertien réel est dit : 1) facialement homogène quand pour toute face $F$ de $\lor$ l’opérateur $δ =$ (Projection sur $F - F$ ) $-$ (Projection sur $F^{⊥} - F^{⊥}$ ) est une dérivation de $\lor$ (i.e. $e^{t δ} \lor = \lor \forall t \in R$ ) ; 2) complexe quand on s’est donné une structure d’algèbre de Lie complexe sur l’algèbre de Lie réelle des dérivations de $\lor$ , modulo son centre. Nous caractérisons les espaces...

Central sequences in the factor associated with Thompson’s group $F$

Paul Jolissaint (1998)

Annales de l'institut Fourier

We prove that the type ${II}_{1}$ factor $L (F)$ generated by the regular representation of $F$ is isomorphic to its tensor product with the hyperfinite type ${II}_{1}$ factor. This implies that the unitary group of $L (F)$ is contractible with respect to the topology defined by the natural Hilbertian norm.

Centrally determined states on von Neumann algebras

Jan Hamhalter (1992)

Mathematica Bohemica

It is shown that every von Neumann algebra whose centre determines the state space is already abelian.

Centrally ergodic one-parameter automorphism groups on semifinite injective von Neumann algebras.

Yasuyuki Kawahigashi (1989)

Mathematica Scandinavica

Chain rules for canonical state extensions on von Neumann algebras

Carlo Cecchini, Dénes Petz (1993)

Colloquium Mathematicae

In previous papers we introduced and studied the extension of a state defined on a von Neumann subalgebra to the whole of the von Neumann algebra with respect to a given state. This was done by using the standard form of von Neumann algebras. In the case of the existence of a norm one projection from the algebra to the subalgebra preserving the given state our construction is simply equivalent to taking the composition with the norm one projection. In this paper we study couples of von Neumann subalgebras...

Character formula for wreath products of compact groups with the infinite symmetric group

Takeshi Hirai, Etsuko Hirai (2006)

Banach Center Publications

Let $G =_{\infty} (T)$ be the wreath product of a compact group T with the infinite symmetric group $_{\infty}$ . We study the characters of factor representations of finite type of G, and give a formula which expresses all the characters explicitly.

Characterisation of matrix-ordered standard forms of W*-algebras.

Gerd Wittstock, Lothar M. Schmitt (1982)

Mathematica Scandinavica

Characterization of L...(M) for injective W*-algebras M.

Lothar M. Schmitt (1985)

Mathematica Scandinavica

Classification of injective factors: The work of Alain Connes.

Wright, Steve (1983)

International Journal of Mathematics and Mathematical Sciences

Closed Derivations in C*-Algebras.

Schôichi Ôta (1981)

Mathematische Annalen

Cohomology of operator algebras. III : reduction to normal cohomology

B.E. Johnson, Richard V. Kadison, John R. Ringrose (1972)

Bulletin de la Société Mathématique de France

Commutators associated to a subfactor and its relative commutants

Hsiang-Ping Huang (2002)

Annales de l’institut Fourier

Let $N \subseteq M$ be an inclusion of $I I_{1}$ factors with finite Jones index. Then $M = (N^{'} \cap M) \oplus [N, M]$ as a vector space. Here $[N, M]$ denotes the vector space spanned by the commutators of the form $[a, b]$ where $a \in N, b \in M$ .

Compact groups of automorphisms of von Neumann algebras.

William L. Geen (1975)

Mathematica Scandinavica

Compactness properties for multiplication operators on von Neumann algebras and their preduals

Stanisław Goldstein, Hans Jarchow, Louis E. Labuschagne (2006)

Banach Center Publications

We consider compactness, weak compactness and complete continuity for multiplication operators on von Neumann algebras and their preduals.

Currently displaying 41 – 60 of 263

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Displaying 41 – 60 of 263

$C^{*}$ algebras associated with von Neumann algebras

Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann

Central sequences in the factor associated with Thompson’s group $F$

Centrally determined states on von Neumann algebras

Centrally ergodic one-parameter automorphism groups on semifinite injective von Neumann algebras.

Chain rules for canonical state extensions on von Neumann algebras

Character formula for wreath products of compact groups with the infinite symmetric group

Characterisation of matrix-ordered standard forms of W*-algebras.

Characterization of L...(M) for injective W*-algebras M.

Classification of injective factors: The work of Alain Connes.

Closed Derivations in C*-Algebras.

Cohomology of operator algebras. III : reduction to normal cohomology

Commutators associated to a subfactor and its relative commutants

Compact groups of automorphisms of von Neumann algebras.

Compactness properties for multiplication operators on von Neumann algebras and their preduals

Comparision of states and Darboux-type properties in von Neumann algebras.

Composition of subfactors : new examples of infinite depth subfactors

Convergence of generalized eigenfunction expansions.

Convolution on the reduced dual of a locally compact group.

Crossed products, direct integrals and Connes' classification of type III factors.

Currently displaying 41 – 60 of 263