The inclusion theorem for multiple summing operators

• Autorzy: David Pérez-García
• Języki publikacji: EN

Abstrakty

EN

We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.

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: 2004
• Tom: 165
• Numer: 3
• Strony: 275-290

Daty

wydano

2004

Twórcy

autor

David Pérez-García

• Área Matemática Aplicada, ESCET, Universidad Rey Juan Carlos, C/ Tulipán s/n, 28933 Mostoles (Madrid), Spain

Identyfikatory

DOI

10.4064/sm165-3-5