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Distortions on Schatten Classes Cp

  • Nicole Tomczak-Jaegermann
Conference paper
Part of the Operator Theory Advances and Applications book series (OT, volume 77)

Abstract

Schatten classes Cp of operators on a Hilbert space are classical non-commutative Banach space analogues of spaces lp. The result by Odell and Schlumprecht [OS] that spaces lp are arbitrarily distortable for 1 <p< ∞, suggests that a similar situation might be true for Schatten classes as well. In this note we prove that it is indeed so: for 1 <p< ∞, spaces Cp are arbitrarily distortable.

Keywords

Orthogonal Projection Successive Operator Partial Isometry Distorted Norm General Banach Space 
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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References

  1. [GK]
    Gohberg, I.C. & Krein, M.G., “Introduction to the theory of linear nonselfadjoint operators” Nauka, Moscow 1963, English translation, AMS 1969.Google Scholar
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    Gowers, W.T. & Maurey, B., The unconditional basic sequence problem, Journal of AMS, 6 (1993), 851–874.MathSciNetzbMATHGoogle Scholar
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    Maurey, B., A remark on distortions, in GAFA Seminar, 1992/93.Google Scholar
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    Maurey, B., Symmetric distortions in l 2ì in GAFA Seminar, 1992/93.Google Scholar
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    Odell, E. & Schlumprecht, T., The distortion problem, preprint.Google Scholar
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    Tomczak-Jaegermann, N., The moduli of smoothness and convexity and the Rademacher averages of trace classes S p , Studia Math., 50 (1974), 163–182.MathSciNetzbMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • Nicole Tomczak-Jaegermann
    • 1
  1. 1.Department of MathematicsUniversity of AlbertaEdmontonAlbertaCanada

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