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Quantification of the reciprocal Dunford-Pettis property

Ondřej F. K. Kalenda, Jiří Spurný (2012)

Studia Mathematica

We prove in particular that Banach spaces of the form C₀(Ω), where Ω is a locally compact space, enjoy a quantitative version of the reciprocal Dunford-Pettis property.

Quantized orthonormal systems: A non-commutative Kwapień theorem

J. García-Cuerva, J. Parcet (2003)

Studia Mathematica

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...

Quantum expanders and geometry of operator spaces

Gilles Pisier (2014)

Journal of the European Mathematical Society

We show that there are well separated families of quantum expanders with asymptotically the maximal cardinality allowed by a known upper bound. This has applications to the “growth" of certain operator spaces: It implies asymptotically sharp estimates for the growth of the multiplicity of M N -spaces needed to represent (up to a constant C > 1 ) the M N -version of the n -dimensional operator Hilbert space O H n as a direct sum of copies of M N . We show that, when C is close to 1, this multiplicity grows as exp β n N 2 for...

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