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# $C^*$-Algebras and Factorization Through Diagonal Operators

Published:2004-12-01
Printed: Dec 2004
• Narcisse Randrianantoanina
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## Abstract

Let $\cal A$ 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 $T:\mathcal{A}\longrightarrow E$, 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 $2  Keywords:$C^*\$-algebras, summing operators, diagonal operators, Radon-Nikodym property
 MSC Classifications: 46L50 - unknown classification 46L5047D15 - unknown classification 47D15