Type and cotype of operator spaces

Hun Hee Lee¹

¹ Department of Pure Mathematics Faculty of Mathematics University of Waterloo 200 University Avenue West Waterloo, Ontario, Canada N2L 3G1

Studia Mathematica, Tome 185 (2008) no. 3, pp. 219-247

Résumé

We consider two operator space versions of type and cotype, namely $S_p$-type, $S_q$-cotype and type $(p,H)$, cotype $(q,H)$ for a homogeneous Hilbertian operator space $H$ and $1\leq p \leq 2 \leq q\leq \infty $, generalizing “$OH$-cotype 2” of G. Pisier. We compute type and cotype of some Hilbertian operator spaces and $L_p$ spaces, and we investigate the relationship between a homogeneous Hilbertian space $H$ and operator spaces with cotype $(2,H)$. As applications we consider operator space versions of generalized little Grothendieck's theorem and Maurey's extension theorem in terms of these new notions.

Détail

DOI : 10.4064/sm185-3-2

Keywords: consider operator space versions type cotype namely p type q cotype type cotype homogeneous hilbertian operator space leq leq leq leq infty generalizing oh cotype pisier compute type cotype hilbertian operator spaces spaces investigate relationship between homogeneous hilbertian space operator spaces cotype applications consider operator space versions generalized little grothendiecks theorem maureys extension theorem terms these notions