We consider two operator space versions of type and cotype, namely -type, -cotype and type (p,H), cotype (q,H) for a homogeneous Hilbertian operator space H and 1 ≤ p ≤ 2 ≤ q ≤ ∞, generalizing “OH-cotype 2” of G. Pisier. We compute type and cotype of some Hilbertian operator spaces and 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-3-2,
author = {Hun Hee Lee},
title = {Type and cotype of operator spaces},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {219-247},
zbl = {1141.47043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-3-2}
}
Hun Hee Lee. Type and cotype of operator spaces. Studia Mathematica, Tome 187 (2008) pp. 219-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-3-2/