Operator spaces and similarity problems.
Factorization of Operators Through Lp ... or Lp1 and Non-Commutative Generalizations.
De nouveaux espaces de Banach sans la propriété d'approximation
Espaces d'opérateurs : une nouvelle dualité
Riesz transforms : a simpler analytic proof of P. A. Meyer's inequality
A new approach to several results of V. Milman.
Some results on Banach spaces without local unconditional structure
Multipliers of the Hardy space H¹ and power bounded operators
We study the space of functions φ: ℕ → ℂ such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that φ(n) = ⟨Tⁿξ,η⟩. This implies that the matrix is a Schur multiplier of B(ℓ₂) or equivalently is in the space (ℓ₁ ⊗̌ ℓ₁)*. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach makes use of a new class of Fourier multipliers of H¹ which we call “shift-bounded”. We show that there is a φ which is a “completely...
Real Interpolation between Row and Column Spaces
We give an equivalent expression for the K-functional associated to the pair of operator spaces (R,C) formed by the rows and columns respectively. This yields a description of the real interpolation spaces for the pair (Mₙ(R),Mₙ(C)) (uniformly over n). More generally, the same result is valid when Mₙ (or B(ℓ₂)) is replaced by any semi-finite von Neumann algebra. We prove a version of the non-commutative Khintchine inequalities (originally due to Lust-Piquard) that is valid for the Lorentz spaces...
Remarques sur les classes de Vapnik-Cervonenkis
Interpolation between H spaces and non-commutative generalizations (II).
We continue an investigation started in a preceding paper. We discuss tha classical result of Carleson connecting Carleson measures with the ∂-equation in a slightly more abstract framework than usual. We also consider a more recent result of Peter Jones which shows the existence of a solution for the ∂-equation, which satisfies simultaneously a good L∞ estimate and a good L1 estimate. This appears as a special case of our main result which can be stated as...
Projections from a von Neumann algebra onto a subalgebra
Une nouvelle classe d'espaces de Banach vérifiant le théorème de Grothendieck
Soit un espace et soit un sous-espace réflexif de dimension infinie de . Nous montrons que le quotient vérifie le théorème de Grothendieck, c’est-à-dire que tout opérateur de dans un espace de Hilbert est 1-sommant; par ailleurs, n’est pas un espace . Cela permet de répondre négativement à une question de Lindenstrauss-Pełczyński ainsi qu’à une question similaire de Grothendieck.
Quantum expanders and geometry of operator spaces
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 -spaces needed to represent (up to a constant ) the -version of the -dimensional operator Hilbert space as a direct sum of copies of . We show that, when is close to 1, this multiplicity grows as for...
Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
Random Fourier series on locally compact abelian groups
Page 1