Quantized orthonormal systems: A non-commutative Kwapień theorem

Simple item page
dc.creatorGarcía-Cuerva, José
dc.creatorParcet, Javier
dc.date2003-12-11
dc.date.accessioned2026-07-07T05:03:50Z
dc.date.available2026-07-07T05:03:50Z
dc.descriptionThe 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 the 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.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0312245
dc.identifierhttp://arxiv.org/abs/math/0312245
dc.identifierStudia Math. 155 (2003), 273-294
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69574
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject46L07; 46C15; 42C15
dc.titleQuantized orthonormal systems: A non-commutative Kwapień theorem
dc.typetext

Files

Collections

arXiv