When weak convergence in von Neumann algebras implies almost uniform convergence?

2026

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DOI 10.1112/blms.70478
Data confidence 70 medium
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Abstract

Abstract We show that weak sequential convergence in a semifinite von Neumann algebra equipped with a faithful normal semifinite trace implies almost uniform convergence if and only if is of type with and that weak sequential convergence in a finite von Neumann algebra with implies (quasi‐)norm convergence in noncommutative spaces associated with for all .