This article is cited in 26 papers

Minimality of Convergence in Measure Topologies on Finite von Neumann Algebras

A. M. Bikchentaev

Kazan State University

Abstract: We prove that the natural embedding of the metric ideal space on a finite von Neumann algebra ${\mathscr M}$ into the $*$-algebra of measurable operators $\widetilde {\mathscr M}$ endowed with the topology of convergence in measure is continuous. Using this fact, we prove that the topology of convergence in measure is a minimal one among all metrizable topologies consistent with the ring structure on $\widetilde {\mathscr M}$.

UDC: 517.986+517.987

Received: 18.12.2002
Revised: 05.08.2003

DOI: 10.4213/mzm36

 English version: Mathematical Notes, 2004, 75:3, 315–321

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