Inventiones mathematicae

, Volume 146, Issue 2, pp 329–363 | Cite as

Continuous family of invariant subspaces for R–diagonal operators

  • Piotr Śniady
  • Roland Speicher


We show that every R–diagonal operator x has a continuous family of invariant subspaces relative to the von Neumann algebra generated by x. This allows us to find the Brown measure of x and to find a new conceptual proof that Voiculescu’s S–transform is multiplicative. Our considerations base on a new concept of R–diagonality with amalgamation, for which we give several equivalent characterizations.


Invariant Subspace Continuous Family Diagonal Operator Equivalent Characterization Conceptual Proof 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Piotr Śniady
    • 1
  • Roland Speicher
    • 2
  1. 1.Institute of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland (e-mail:
  2. 2.Department of Mathematics and Statistics, Queens University, Kingston Ontario K7L 3N6, Canada (e-mail:

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