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Gilles Pisier
, 2014

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...lves the growth of a sequence of integers N 7→ KE(N,C) attached to an operator space E (and a constant C > 1), in a way that is similar but seems different from the number kE(N,C) introduced by us in =-=[25]-=-. We denote by KE(N,C) the smallest K such that there is a linear embedding f : E →MK satisfying ∀x ∈MN (E) ‖(Id⊗ f)(x)‖MN (MK) ≤ ‖x‖MN (E) ≤ C‖(Id⊗ f)(x)‖MN (MN ). The latter sequence is bounded iff ...

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Gilles Pisier, Universite ́ Paris Vi
, 2014

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...es Pisier Texas A&M University College Station, TX 77843, U. S. A. and Université Paris VI IMJ, Equipe d’Analyse Fonctionnelle, Case 186, 75252 Paris Cedex 05, France May 5, 2014 In this appendix to =-=[5]-=- we give a quick proof of an inequality that can be substituted to Hastings’s result from [2], quoted as Lemma 1.9 in [5]. Our inequality is less sharp but also appears to apply with more general (and...

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Gilles Pisier, Universite ́ Paris Vi
, 2014

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...n, TX 77843, U. S. A. and Université Paris VI IMJ, Equipe d’Analyse Fonctionnelle, Case 186, 75252 Paris Cedex 05, France May 5, 2014 Abstract This is a supplement to our previous paper on the arxiv =-=[13]-=-. We show that there is a non-exact C∗-algebra that is 1-subexponential, and we give several other complements to the results of that paper. Our example can be described very simply using random matri...

by
Gilles Pisier
, 2014

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...ance d. For the operator space case in §3, the general structure of our argument is modeled on that of §1. However, the ingredients are more involved. We make crucial use of our previous results from =-=[22]-=- on quantum expanders, and we carefully explain in §4 why they are needed in the matricial case. Remark 0.1. I am grateful to S. Szarek for the following information. The upper bound in (0.1) is known...

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... it suffices to know for our present purpose that C(n) < n for infinitely many n’s or even merely for some n. This can be proved in several ways for which we refer the reader to [7] or [10]. See also =-=[12]-=- for a more recent-somewhat more refined-approach. For any integer n ≥ 1, the constant C(n) is defined as follows: C(n) is the smallest constant C such that for each m ≥ 1, there is Nm ≥ 1 and an n-tu...

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