We show that, if a a finite-dimensional operator space E is such that X contains E C-completely isomorphically whenever X** contains E completely isometrically, then E is -completely isomorphic to Rₘ ⊕ Cₙ for some n, m ∈ ℕ ∪ 0. The converse is also true: if X** contains Rₘ ⊕ Cₙ λ-completely isomorphically, then X contains Rₘ ⊕ Cₙ (2λ + ε)-completely isomorphically for any ε > 0.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-2-5,
author = {Alvaro Arias and Timur Oikhberg},
title = {Embeddings of finite-dimensional operator spaces into the second dual},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {181-198},
zbl = {1131.46037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-2-5}
}
Alvaro Arias; Timur Oikhberg. Embeddings of finite-dimensional operator spaces into the second dual. Studia Mathematica, Tome 178 (2007) pp. 181-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm181-2-5/