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Inventiones mathematicae

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

Continuous family of invariant subspaces for R–diagonal operators

  • Piotr Śniady
  • Roland Speicher

Abstract.

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.

Keywords

Invariant Subspace Continuous Family Diagonal Operator Equivalent Characterization Conceptual Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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: Piotr.Sniady@math.uni.wroc.pl)PL
  2. 2.Department of Mathematics and Statistics, Queens University, Kingston Ontario K7L 3N6, Canada (e-mail: speicher@mast.queensu.ca)CA

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