JournalszaaVol. 21, No. 3pp. 709–717

Comparison of Non-Commutative 2- and pp-Summing Operators from B(l2)B(l_2) into OHOH

  • L. Mezrag

    M'Sila University, Tunisia
Comparison of Non-Commutative 2- and $p$-Summing Operators from $B(l_2)$ into $OH$ cover
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Abstract

In the theory of pp-summing operators studied by Pietsch we know that π2(C(K),H)=πp(C(K),H)\pi_2(C(K),H) = \pi_p(C(K),H) for any Hilbert space HH and any pp such that 2<p<+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. πl2(Bl2),OH)(=π20(B(l2),OH))πlp(B(l2),OH)\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 pp-Summing Operators from B(l2)B(l_2) into OHOH. Z. Anal. Anwend. 21 (2002), no. 3, pp. 709–717

DOI 10.4171/ZAA/1104