Real Interpolation between Row and Column Spaces

Gilles Pisier. "Real Interpolation between Row and Column Spaces." Bulletin of the Polish Academy of Sciences. Mathematics 59.3 (2011): 237-259. <http://eudml.org/doc/286611>.

@article{GillesPisier2011,
abstract = {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.},
author = {Gilles Pisier},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {real interpolation method; row and column operator space; K-functional; non-commutative Khintchine inequality; non-commutative Lorentz space},
language = {eng},
number = {3},
pages = {237-259},
title = {Real Interpolation between Row and Column Spaces},
url = {http://eudml.org/doc/286611},
volume = {59},
year = {2011},
}

TY - JOUR
AU - Gilles Pisier
TI - Real Interpolation between Row and Column Spaces
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2011
VL - 59
IS - 3
SP - 237
EP - 259
AB - 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.
LA - eng
KW - real interpolation method; row and column operator space; K-functional; non-commutative Khintchine inequality; non-commutative Lorentz space
UR - http://eudml.org/doc/286611
ER -