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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Embeddings of finite-dimensional operator spaces into the second dual

### Tom 181 / 2007

Studia Mathematica 181 (2007), 181-198 MSC: 46L07, 47L25. DOI: 10.4064/sm181-2-5

#### Streszczenie

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 $2^{15} C^{11}$-completely isomorphic to $\mathbf{R}_m \oplus \mathbf{C}_n$ for some $n, m \in \mathbb N \cup \{0\}$. The converse is also true: if $X^{**}$ contains $\mathbf{R}_m \oplus \mathbf{C}_n$ $\lambda$-completely isomorphically, then $X$ contains $\mathbf{R}_m \oplus \mathbf{C}_n$ $(2\lambda+\varepsilon)$-completely isomorphically for any $\varepsilon > 0$.

#### Autorzy

• Alvaro AriasDepartment of Mathematics
University of Denver
Denver, CO 80208, U.S.A.
e-mail
• Timur OikhbergDepartment of Mathematics
The University of California at Irvine
Irvine, CA 92697-3875, U.S.A
e-mail

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