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/