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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 3, 2002, pp. 709–717
DOI: 10.4171/ZAA/1104

Published online: 2002-09-30

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

L. Mezrag[1]

(1) M'Sila University, Tunisia

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

Keywords: Operator spaces, completely bounded operators, $p$-summing operators

Mezrag L.: Comparison of Non-Commutative 2- and $p$-Summing Operators from $B(l_2)$ into $OH$. Z. Anal. Anwend. 21 (2002), 709-717. doi: 10.4171/ZAA/1104