Geodesic
Embeddings of finite-dimensional operator spaces into the second dual
Alvaro Arias 1   ; Timur Oikhberg 2
1 Department of Mathematics University of Denver Denver, CO 80208, U.S.A.
2 Department of Mathematics The University of California at Irvine Irvine, CA 92697-3875, U.S.A
Studia Mathematica, Tome 181 (2007) no. 2, pp. 181-198 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\varepsilon > 0$.
DOI : 10.4064/sm181-2-5
Keywords: finite dimensional operator space contains c completely isomorphically whenever ** contains completely isometrically completely isomorphic mathbf oplus mathbf mathbb cup converse ** contains mathbf oplus mathbf lambda completely isomorphically contains mathbf oplus mathbf lambda varepsilon completely isomorphically varepsilon

Alvaro Arias  1   ; Timur Oikhberg  2

1 Department of Mathematics University of Denver Denver, CO 80208, U.S.A.
2 Department of Mathematics The University of California at Irvine Irvine, CA 92697-3875, U.S.A 
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Alvaro Arias; Timur Oikhberg. Embeddings of finite-dimensional operator spaces
into the second dual. Studia Mathematica, Tome 181 (2007) no. 2, pp. 181-198. doi: 10.4064/sm181-2-5

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