Quantized orthonormal systems: A non-commutative Kwapień theorem

J. García-Cuerva, and J. Parcet. "Quantized orthonormal systems: A non-commutative Kwapień theorem." Studia Mathematica 155.3 (2003): 273-294. <http://eudml.org/doc/284791>.

@article{J2003,
abstract = {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.},
author = {J. García-Cuerva, J. Parcet},
journal = {Studia Mathematica},
keywords = {operator space; Kwapień theorem; quantized system; Riesz type; Rademacher system; Gauss system},
language = {eng},
number = {3},
pages = {273-294},
title = {Quantized orthonormal systems: A non-commutative Kwapień theorem},
url = {http://eudml.org/doc/284791},
volume = {155},
year = {2003},
}

TY - JOUR
AU - J. García-Cuerva
AU - J. Parcet
TI - Quantized orthonormal systems: A non-commutative Kwapień theorem
JO - Studia Mathematica
PY - 2003
VL - 155
IS - 3
SP - 273
EP - 294
AB - 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.
LA - eng
KW - operator space; Kwapień theorem; quantized system; Riesz type; Rademacher system; Gauss system
UR - http://eudml.org/doc/284791
ER -