Mathematische Annalen

, Volume 316, Issue 1, pp 61–82

Compressions of free products of von Neumann algebras

Authors

  • Kenneth J. Dykema
    • Department of Mathematics, Texas A&M University, College Station, TX 77843, USA (e-mail: Ken.Dykema@math.tamu.edu)
  • Florin Radulescu
    • Depatment of Mathematics, University of Iowa, Iowa City IA 52242–1466, USA (e-mail: radulesc@math.uiowa.edu)
Original article

DOI: 10.1007/s002080050004

Cite this article as:
Dykema, K. & Radulescu, F. Math Ann (2000) 316: 61. doi:10.1007/s002080050004

Abstract.

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

Copyright information

© Springer-Verlag Berlin Heidelberg 2000