Comparison of Non-Commutative 2- and $p$-Summing Operators from $B(l_2)$ into $OH$

Abstract

In the theory of $p$-summing operators studied by Pietsch we know that ${\pi }_2(C(K),H)={\pi }_p(C(K),H)$ for any Hilbert space $H$ and any $p$ such that $2<p<+\infty$. In this paper we prove that this equality is not true in the same notion generalized by Junge and Pisier to operator spaces, i.e. ${\pi }_{l_2}(B{l}_2),OH)(={\pi }_2^0(B(l_2),OH))\ne {\pi }_{l_p}(B(l_2),OH)$.