Random Matrices and Subexponential Operator Spaces
Abstract
We introduce and study a generalization of the notion of exact operator space that we call subexponential. Using Random Matrices we show that the factorization results of Grothendieck type that are known in the exact case all extend to the subexponential case, but we exhibit (a continuum of distinct) examples of non-exact subexponential operator spaces, as well as a -algebra that is subexponential with constant 1 but not exact. We also show that , and (or any other maximal operator space) are not subexponential.
Cite
@article{arxiv.1212.2053,
title = {Random Matrices and Subexponential Operator Spaces},
author = {Gilles Pisier},
journal= {arXiv preprint arXiv:1212.2053},
year = {2014}
}
Comments
This paper is extracted from an older version of "Quantum expanders and geometry of operator spaces". v2: Some corrections. A notable addition is Theorem 7.13, due to Mikael de la Salle, showing that the C* algebra generated by the block direct sum of unitary random matrices is a.s. subexponential with constant 1, in analogy with what we proved in the Gaussian case. v3: minor corrections