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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.

References [Enhancements On Off] (What's this?)

  • 1. L. Ge, On maximal injective subalgebras of factors, Adv. Math. 118 (1996), 34-70.
  • 2. H. Halpern, V. Kaftal and G.Weiss, The relative Dixmier property in discrete crossed products, J. Funct. Anal. 69 (1986), 121-140. MR 87k:46137
  • 3. R. V. Kadison and I. M. Singer, Extensions of pure states, Amer. J. Math. 81 (1959), 383-400. MR 23:A1243
  • 4. R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras, vol. II, Academic Press, New York, 1986. MR 88d:46106
  • 5. S. Popa, On a problem of R. V. Kadison on maximal abelian $*$-subalgebras in factors, Invent. Math. 65 (1981), 269-281. MR 83g:46056
  • 6. -, Markov traces on universal Jones algebras and subfactors of finite index, Invent. Math. 111 (1993), 375-405. MR 94c:46128
  • 7. -, Free-independent sequences in type $\mathbf{II}_1$ factors and related problems, Astérisque, 232 (1995), 187-202. MR 97b:46080
  • 8. M. Takesaki, On the singularity of a positive linear functional on operator algebras, Proc. Jap. Acad. 35 (1959), 365-366. MR 22:3991
  • 9. D. V. Voiculescu, K. J. Dykema and A. Nica, Free random variables, CRM Monograph Series, vol.1, AMS, Providence RI, 1992. MR 94c:46133

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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

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

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