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

L. Mezrag

doi:10.4171/zaa/1104

JournalszaaVol. 21, No. 3pp. 709–717

Comparison of Non-Commutative 2- and $p$ -Summing Operators from $B (l_{2})$ into $O H$

L. Mezrag
M'Sila University, Tunisia

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Abstract

In the theory of $p$ -summing operators studied by Pietsch we know that $π_{2} (C (K), H) = π_{p} (C (K), H)$ 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. $π_{l_{2}} (B l_{2}), O H) (= π_{2}^{0} (B (l_{2}), O H)) \neq = π_{l_{p}} (B (l_{2}), O H)$ .

Cite this article

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

DOI 10.4171/ZAA/1104