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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-3-6,
author = {Gilles Pisier},
title = {Real Interpolation between Row and Column Spaces},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {59},
year = {2011},
pages = {237-259},
zbl = {1245.46047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-3-6}
}
Gilles Pisier. Real Interpolation between Row and Column Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) pp. 237-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-3-6/