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A+ CATEGORY SCIENTIFIC UNIT

Multiple summing operators on spaces

Volume 225 / 2014

Dumitru Popa Studia Mathematica 225 (2014), 9-28 MSC: Primary 47H60; Secondary 46B25, 46C99. DOI: 10.4064/sm225-1-2

Abstract

We use the Maurey–Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of l_{p} spaces. This characterization is used to show that multiple s-summing operators on a product of l_{p} spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 \leq s \leq 2). We use these results to show that there exist many natural multiple s-summing operators T:l_{4/3}\times l_{{4}/{3}}\rightarrow l_{2} such that none of the associated linear operators is s-summing (1 \leq s \leq 2). Further we show that if n\geq 2, there exist natural bounded multilinear operators T:l_{{2n}/{(n+1)}}\times \cdots \times l_{{2n}/{(n+1)}}\rightarrow l_{2} for which none of the associated multilinear operators is multiple s-summing (1 \leq s \leq 2).

Authors

  • Dumitru PopaDepartment of Mathematics
    Ovidius University of Constanţa
    Bd. Mamaia 124
    900527 Constanţa, Romania
    e-mail

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