Quantized orthonormal systems: A non-commutative Kwapień theorem

Tom 155 / 2003

J. García-Cuerva, J. Parcet Studia Mathematica 155 (2003), 273-294 MSC: 46L07, 46C15, 42C15. DOI: 10.4064/sm155-3-6

Streszczenie

The concepts of Riesz type and cotype of a given Banach space are extended to a non-commutative setting. First, the Banach space is replaced by an operator space. The notion of quantized orthonormal system, which plays the role of an orthonormal system in the classical setting, is then defined. The Fourier type and cotype of an operator space with respect to a non-commutative compact group fit in this context. Also, the quantized analogs of Rademacher and Gaussian systems are treated. All this is used to obtain an operator space version of the classical theorem of Kwapień characterizing Hilbert spaces by means of vector-valued orthogonal series. Several approaches to this result with different consequences are given.

Autorzy

  • J. García-CuervaDepartamento de Matemáticas, C-XV
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
    e-mail
  • J. ParcetDepartamento de Matemáticas, C-XV
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
    e-mail

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