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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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