Multiple summing operators on $l_{p}$ spaces

• Autorzy: Dumitru Popa
• Języki publikacji: EN

Abstrakty

EN

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 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators $T: l_{4/3} × l_{4/3} → l₂$ such that none of the associated linear operators is s-summing (1 ≤ s ≤ 2). Further we show that if n ≥ 2, there exist natural bounded multilinear operators $T: l_{2n/(n+1)} × ⋯ × l_{2n/(n+1)} → l₂$ for which none of the associated multilinear operators is multiple s-summing (1 ≤ s ≤ 2).

Kategorie tematyczne

• 46C99: None of the above, but in this section
• 46B25: Classical Banach spaces in the general theory
• 47H60: Multilinear and polynomial operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 225
• Numer: 1
• Strony: 9-28

Daty

wydano

2014

Twórcy

autor

Dumitru Popa

• Department of Mathematics, Ovidius University of Constanţa, Bd. Mamaia 124, 900527 Constanţa, Romania

Identyfikatory

DOI

10.4064/sm225-1-2