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B-convex operator spaces
Javier Parcet
The notion of B-convexity for operator spaces, which a priori depends on a set of parameters indexed by , is defined. Some of the classical characterizations of this geometric n…
Quantized orthonormal systems: A non-commutative Kwapień theorem
José García-Cuerva, Javier Parcet
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 qua…
Non-commutative Khintchine type inequalities associated with free groups
Javier Parcet, Gilles Pisier
Let $\Free_n$ denote the free group with generators . Let stand for the left regular representation of $\Free_n$ and let be the standard trace assoc…
Multi-indexed p-orthogonal sums in non-commutative Lebesgue spaces
Javier Parcet
In this paper we extend a recent Pisier's inequality for p-orthogonal sums in non-commutative Lebesgue spaces. To that purpose, we generalize the notion of p-orthogonality to the c…