286 citations · 878 across the 61 of their papers we have counts for
35 papers · 1 filter
Operator space theory from the maximal viewpoint
Gilles Pisier, Jean Roydor
We initiate a theory of ``operator spaces" (in other words subspaces of -algebras) with an emphasis on the maximal tensor product. The natural morphisms become the maximally b…
The lifting property for -algebras : from local to global ?
Gilles Pisier
This note is motivated by Kirchberg's conjecture that the local lifting property (LLP) implies the lifting property (LP) for -algebras. The author recently constructed by a "l…
Operator spaces with the WEP, the OLLP and the Gurarii property
Gilles Pisier
We construct non-exact operator spaces satisfying the Weak Expectation Property (WEP) and the Operator space version of the Local Lifting Property (OLLP). These examples should be…
Seemingly injective von Neumann algebras
Gilles Pisier
We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of t…
On the Lifting Property for -algebras
Gilles Pisier
We characterize the lifting property (LP) of a separable -algebra by a property of its maximal tensor product with other -algebras, namely we prove that has the L…
A non-nuclear -algebra with the Weak Expectation Property and the Local Lifting Property
Gilles Pisier
We construct the first example of a -algebra with the properties in the title. This gives a new example of non-nuclear for which there is a unique -norm on $A \ot…
On a Characterization of the Weak Expectation Property (WEP)
Gilles Pisier
We give a detailed proof of a new characterization of the Weak Expectation Property (WEP) announced by Haagerup in the 1990's but unavailable (in any form) till now. Our main resul…
On a linearization trick
Gilles Pisier
In several situations, mainly involving a self-adjoint set of unitary generators of a -algebra, we show that any matrix polynomial in the generators and the unit that is in th…
Interpolation and Fatou-Zygmund property for completely Sidon subsets of discrete groups (New title: Completely Sidon sets in discrete groups)
Gilles Pisier
A subset of a discrete group is called completely Sidon if its span in is completely isomorphic to the operator space version of the space (i.e. equi…
Completely Sidon sets in -algebras (New title)
Gilles Pisier
A sequence in a -algebra is called completely Sidon if its span in is completely isomorphic to the operator space version of the space (i.e. equipped…
Quantum expanders and growth of group representations
Gilles Pisier
Let be a finite dimensional unitary representation of a group with a generating symmetric -element set . Fix $\vp>0$. Assume that the spectrum of $|S|^{-1}\s…
The non-commutative Khintchine inequalities for p<1
Gilles Pisier, Eric Ricard
We give a proof of the Khintchine inequalities in non-commutative -spaces for all . These new inequalities are valid for the Rademacher functions or Gaussian random va…
A continuum of -norms on $\IB(H)\otimes \IB(H)$ and related tensor products
Narutaka Ozawa, Gilles Pisier
For any pair of von Neumann algebras such that the algebraic tensor product admits more than one -norm, the cardinal of the set of -n…
Random Matrices and Subexponential Operator Spaces
Gilles Pisier
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 Grothendi…
Examples of non exact 1-subexponential -algebras
Gilles Pisier
This is a complement to our previous paper on the arxiv on quantum expanders and geometry of operator spaces. We show that there is a non-exact -algebra that is 1-subexponenti…
Quantum Expanders and Geometry of Operator Spaces II
Gilles Pisier
In this appendix to our paper with the same title posted on arxiv we give a quick proof of an inequality that can be substituted to Hastings's result, quoted as Lemma 1.9 in our pr…
Quantum Expanders and Geometry of Operator Spaces
Gilles Pisier
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…
Martingale inequalities and Operator space structures on
Gilles Pisier
We describe a new operator space structure on when is an even integer and compare it with the one introduced in our previous work using complex interpolation. For the new…
Tripartite Bell inequality, random matrices and trilinear forms
Gilles Pisier
In this seminar report, we present in detail the proof of a recent result due to J. Briët and T. Vidick, improving an estimate in a 2008 paper by D. Pérez-Garc\'ıa, M. Wolf, C. Pal…
Strong convergence for reduced free products (Remarks on a result by Paul Skoufranis)
Gilles Pisier
Using an inequality due to Ricard and Xu, we give a different proof of Paul Skoufranis's recent result showing that the strong convergence of possibly non-commutative random variab…
On the Dixmier problem (Seminar report after Monod-Ozawa, JFA 2010)
Gilles Pisier
This seminar report contains a detailed account of the proof of the main results in Monod and Ozawa's recent JFA paper on the Dixmier unitarizability problem. The proof is exactly…
Real interpolation between row and column spaces
Gilles Pisier
We give an equivalent expression for the -functional associated to the pair of operator spaces formed by the rows and columns respectively. This yields a description of…
Remarks on the non-commutative Khintchine inequalities for
Gilles Pisier
We show that the validity of the non-commutative Khintchine inequality for some with implies its validity (with another constant) for all . We prove this for…
Simultaneous similarity, bounded generation and amenability
Gilles Pisier
We prove that a discrete group is amenable iff it is strongly unitarizable in the following sense: every unitarizable representation on can be unitarized by an invertib…