Type and cotype of operator spaces

Hun Hee Lee. "Type and cotype of operator spaces." Studia Mathematica 185.3 (2008): 219-247. <http://eudml.org/doc/284984>.

@article{HunHeeLee2008,
abstract = {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 ≤ p ≤ 2 ≤ q ≤ ∞, 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.},
author = {Hun Hee Lee},
journal = {Studia Mathematica},
keywords = {completely summing maps; operator space; cotype},
language = {eng},
number = {3},
pages = {219-247},
title = {Type and cotype of operator spaces},
url = {http://eudml.org/doc/284984},
volume = {185},
year = {2008},
}

TY - JOUR
AU - Hun Hee Lee
TI - Type and cotype of operator spaces
JO - Studia Mathematica
PY - 2008
VL - 185
IS - 3
SP - 219
EP - 247
AB - 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 ≤ p ≤ 2 ≤ q ≤ ∞, 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.
LA - eng
KW - completely summing maps; operator space; cotype
UR - http://eudml.org/doc/284984
ER -