Abstract
Let $A$ be a $C^*$-algebra. It is shown that every absolutely summing operator from $A$ into $\ell_2$ factors through a Hilbert space operator that belongs to the 4-Schatten- von Neumann class. We also provide finite dimensinal examples that show that one can not improve the 4-Schatten-von Neumann class to $p$-Schatten von Neumann class for any $p 0$, the $\epsilon$-capacity of the image of the unit ball of $A$ under $T$ does not exceed $N(\epsilon)$. This aswers positively a question raised by Pe\l czynski.
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