Real Interpolation between Row and Column Spaces Academic Article uri icon

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 $(M_n(R), M_n(C))$ (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 $L_{p,q}( au)$ associated to a non-commutative measure $ au$, simultaneously for the whole range $1le p,q< infty$, regardless whether $p<2 $ or $p>2$. Actually, the main novelty is the case $p=2,q
    ot=2$. We also prove a certain simultaneous decomposition property for the operator norm and the Hilbert-Schmidt one.

author list (cited authors)

  • Pisier, G.

citation count

  • 2

publication date

  • January 2011