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Singular extensions of the trace
and the relative Dixmier property
in the type $\mathrm{II}_1$ factors

Author: Florin Pop
Journal: Proc. Amer. Math. Soc. 126 (1998), 2987-2992
MSC (1991): Primary 46L10, 46L30
MathSciNet review: 1452820
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Abstract: If $ N \subset M $ is an inclusion of type $\mathrm{II}_1$ factors with $ N'\cap M = \mathbf{C} I,$ we study the connection between the existence of singular states on $M$ which extend the trace on $N$ and the Dixmier approximation property in $M$ with unitaries in $N.$ We also prove the existence of singular conditional expectations from certain free product factors onto irreducible hyperfinite subfactors.

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Florin Pop
Affiliation: Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska 68588
Address at time of publication: Division of Mathematical Science, 241 Schaeffer Hall, University of Iowa, Iowa City, Iowa 52242

Received by editor(s): February 24, 1997
Received by editor(s) in revised form: March 10, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society