Mathematische Annalen

, Volume 316, Issue 1, pp 61–82 | Cite as

Compressions of free products of von Neumann algebras

  • Kenneth J. Dykema
  • Florin Radulescu
Original article


A reduction formula for compressions of von Neumann algebra II\(_1\)–factors arising as free products is proved. This shows that the fundamental group is \({\bf R}^*_+\) for some such algebras. Additionally, by taking a sort of free product with an unbounded semicircular element, continuous one parameter groups of trace scaling automorphisms on II\(_\infty\)–factors are constructed; this produces type III\(_1\) factors with core \(\mathcal{M}\otimes B(\mathcal{H})\), where \(\mathcal{M}\) can be a full II\(_1\)–factor without the Haagerup approximation property.

Mathematics Subject Classification (1991):46L35, 46L40 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Kenneth J. Dykema
    • 1
  • Florin Radulescu
    • 2
  1. 1.Department of Mathematics, Texas A&M University, College Station, TX 77843, USA (e-mail: US
  2. 2.Depatment of Mathematics, University of Iowa, Iowa City IA 52242–1466, USA (e-mail: US

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