Bundle Convergence in a von Neumann Algebra and in a von Neumann Subalgebra
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 283-295
MSC: Primary 46L53, 46L10.
DOI: 10.4064/ba52-3-8
Abstract
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 ${\mathcal A}$.
