Geodesic
${{C}^{*}}$ -Algebras and Factorization Through Diagonal Operators
Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 615-623

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DOI

Let $\mathcal{A}$ be a ${{C}^{*}}$ -algebra and $E$ be a Banach space with the Radon-Nikodym property. We prove that if $j$ is an embedding of $E$ into an injective Banach space then for every absolutely summing operator $T:\,\mathcal{A}\,\to \,E$ , the composition $j\,\circ \,T$ factors through a diagonal operator from ${{l}^{2}}$ into ${{l}^{1}}$ . In particular, $T$ factors through a Banach space with the Schur property. Similarly, we prove that for $2\,<\,p\,<\,\infty $ , any absolutely summing operator from $\mathcal{A}$ into $E$ factors through a diagonal operator from ${{l}^{p}}$ into ${{l}^{2}}$ .
DOI : 10.4153/CMB-2004-059-9
Mots-clés : 46L50, 47D15, C *-algebras, summing operators, diagonal operators, Radon-Nikodym property 
Randrianantoanina, Narcisse. ${{C}^{*}}$ -Algebras and Factorization Through Diagonal Operators. Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 615-623. doi: 10.4153/CMB-2004-059-9
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     title = {${{C}^{*}}$ {-Algebras} and {Factorization} {Through} {Diagonal} {Operators}},
     journal = {Canadian mathematical bulletin},
     pages = {615--623},
     year = {2004},
     volume = {47},
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     doi = {10.4153/CMB-2004-059-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-059-9/}
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