Real Interpolation between Row and Column Spaces

• Autorzy: Gilles Pisier
• Języki publikacji: EN

Abstrakty

EN

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 $L_{p,q}(τ)$ associated to a non-commutative measure τ, simultaneously for the whole range 1 ≤ p,q < ∞, regardless of whether p < 2 or p > 2. Actually, the main novelty is the case p = 2, q ≠ 2. We also prove a certain simultaneous decomposition property for the operator norm and the Hilbert-Schmidt norm.

Kategorie tematyczne

• 46L07: Operator spaces and completely bounded maps
• 46B70: Interpolation between normed linear spaces
• 47L25: Operator spaces (= matricially normed spaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: 59
• Numer: 3
• Strony: 237-259

Daty

wydano

2011

Twórcy

autor

Gilles Pisier

• Mathematics Department, Texas A&M University, College Station, TX 77843, U.S.A.
• Université Paris VI, Institut Mathématique de Jussieu, Analyse Fonctionnelle, Case 186, 75252 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/ba59-3-6