Quantized orthonormal systems: A non-commutative Kwapień theorem

• Autorzy: J. García-Cuerva , J. Parcet
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L07: Operator spaces and completely bounded maps
• 42C15: General harmonic expansions, frames
• 46C15: Characterizations of Hilbert spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 3
• Strony: 273-294

Daty

wydano

2003

Twórcy

autor

J. García-Cuerva

• Departamento de Matemáticas, C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain

autor

J. Parcet

• Departamento de Matemáticas, C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Identyfikatory

DOI

10.4064/sm155-3-6