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

### L. Mezrag

M'Sila University, Tunisia

## 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. $\pi_{l_2} (Bl_2), OH) (=\pi^0_2(B(l_2),OH)) \neq \pi_{l_p}(B(l_2),OH)$.

## Cite this article

L. Mezrag, Comparison of Non-Commutative 2- and $p$-Summing Operators from $B(l_2)$ into $OH$. Z. Anal. Anwend. 21 (2002), no. 3, pp. 709–717

DOI 10.4171/ZAA/1104