Singular extensions of the trace and the relative Dixmier property in the type $II_1$ factors
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- by Florin Pop PDF
- Proc. Amer. Math. Soc. 126 (1998), 2987-2992 Request permission
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.References
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Additional Information
- 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
- MR Author ID: 254337
- Email: fpop@stat.uiowa.edu
- Received by editor(s): February 24, 1997
- Received by editor(s) in revised form: March 10, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2987-2992
- MSC (1991): Primary 46L10, 46L30
- DOI: https://doi.org/10.1090/S0002-9939-98-04401-3
- MathSciNet review: 1452820