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10. The Kadison Similarity Problem

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

Abstract

This chapter concentrates on the (still open) Kadison Similarity problem (= Problem 0.2). We show that this problem is equivalent to several seemingly different questions which appeared in other contexts: Arveson’s hyperreflexivity problem and Dixmier’s invariant opemtor range problem. Finally, we describe the author’s recent work on the notion of “length” of an opemtor algebm, which also leads to one more reformulation of Kadison’s question.

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). 10. The Kadison 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_11

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  • DOI: https://doi.org/10.1007/978-3-540-44563-0_11

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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