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.
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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
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