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

http://dx.doi.org/10.4153/CMB-2004-059-9
Canad. Math. Bull. 47(2004), 615-623

  Published:2004-12-01
 Printed: Dec 2004

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 $C^*$-algebras, summing operators, diagonal operators, Radon-Nikodym property

MSC Classifications:

46L50, 47D15 show english descriptions unknown classification 46L50 unknown classification 47D15 46L50 - unknown classification 46L50 47D15 - unknown classification 47D15