Real Interpolation between Row and Column Spaces

Tom 59 / 2011

Gilles Pisier Bulletin Polish Acad. Sci. Math. 59 (2011), 237-259 MSC: 46L07, 47L25, 46B70. DOI: 10.4064/ba59-3-6


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 $(M_n(R), M_n(C))$ (uniformly over $n$). More generally, the same result is valid when $M_n$ (or $B(\ell _2)$) 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 $L_{p,q}(\tau )$ associated to a non-commutative measure $\tau $, simultaneously for the whole range $1\le p,q< \infty $, regardless of whether $p<2 $ or $p>2$. Actually, the main novelty is the case $p=2$, $q\not =2$. We also prove a certain simultaneous decomposition property for the operator norm and the Hilbert–Schmidt norm.


  • Gilles PisierMathematics 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

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek