Bundle Convergence in a von Neumann Algebra and in a von Neumann Subalgebra

Barthélemy Le Gac ¹   ; Ferenc Móricz ²

¹ Université de Provence Centre de Mathématiques et Informatique 39 rue Joliot-Curie 13453 Marseille Cedex 13, France
² Bolyai Institute University of Szeged Aradi vértanúk tere 1 6720 Szeged, Hungary

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 3, pp. 283-295

Résumé

Let $H$ be a separable complex Hilbert space, ${\mathcal A}$ a von Neumann algebra in ${\mathcal L}(H)$, $\phi $ a faithful, normal state on ${\mathcal A}$, and ${\mathcal B}$ a commutative von Neumann subalgebra of ${\mathcal A}$. Given a sequence $(X_n: n\ge 1)$ of operators in ${\mathcal B}$, we examine the relations between bundle convergence in ${\mathcal B}$ and bundle convergence in ${\mathcal A}$.

Détail

DOI : 10.4064/ba52-3-8

Mots-clés : separable complex hilbert space mathcal von neumann algebra mathcal phi faithful normal state mathcal mathcal commutative von neumann subalgebra mathcal given sequence operators mathcal examine relations between bundle convergence mathcal bundle convergence mathcal