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

Volume 52 / 2004

Barthélemy Le Gac, Ferenc Móricz Bulletin Polish Acad. Sci. Math. 52 (2004), 283-295 MSC: Primary 46L53, 46L10. DOI: 10.4064/ba52-3-8


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 ${\mathcal A}$.


  • Barthélemy Le GacUniversité de Provence
    Centre de Mathématiques et Informatique
    39 rue Joliot-Curie
    13453 Marseille Cedex 13, France
  • Ferenc MóriczBolyai Institute
    University of Szeged
    Aradi vértanúk tere 1
    6720 Szeged, Hungary

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