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9. The Sz.-Nagy-Halmos similarity problem

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1618)

Abstract

We present the author’s recent counterexample to the Halmos similarity problem (described above as Problem 0.3): there is a polynomially bounded operator on Hilbert space which is not similar to a contraction. We also include two related finite dimensional estimates related to n x n-matrices. For one of them, the estimate for polynomially bounded n x n-matrices, the sharp order of growth, when n tends to infinity, is not yet known.

Mathematics Subject Classification (2000):

  • primary 47AO5
  • 46LO5
  • 43A65 secondary 47A20
  • 47B 10
  • 42B30
  • 46E40
  • 46L57
  • 47C 15
  • 47L20

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Correspondence to Gilles Pisier .

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© 2001 Springer-Verlag Berlin/Heidelberg

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Pisier, G. (2001). 9. The Sz.-Nagy-Halmos similarity problem. In: Similarity Problems and Completely Bounded Maps. Lecture Notes in Mathematics, vol 1618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44563-0_10

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  • DOI: https://doi.org/10.1007/978-3-540-44563-0_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41524-4

  • Online ISBN: 978-3-540-44563-0

  • eBook Packages: Springer Book Archive