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

[摘要] Let $cal A$ be a $C^*$-algebra and $E$ be a Banach space withthe Radon-Nikodym property. We prove that if $j$ is an embeddingof $E$ into an injective Banach space then for every absolutelysumming 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 withthe Schur property. Similarly, we prove that for $2

[学科分类] 数学（综合）

[关键词] $C^*$-algebras;summing operators;diagonal operators;Radon-Nikodym property