Cotype and absolutely summing homogeneous polynomials in $ℒ_{p}$ spaces

• Autorzy: Daniel Pellegrino
• Języki publikacji: EN

Abstrakty

EN

We lift to homogeneous polynomials and multilinear mappings a linear result due to Lindenstrauss and Pełczyński for absolutely summing operators. We explore the notion of cotype to obtain stronger results and provide various examples of situations in which the space of absolutely summing homogeneous polynomials is different from the whole space of homogeneous polynomials. Among other consequences, these results enable us to obtain answers to some open questions about absolutely summing homogeneous polynomials and multilinear mappings on $ℒ_{∞}$ spaces.

Kategorie tematyczne

• 46G25: (Spaces of) multilinear mappings, polynomials
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 157
• Numer: 2
• Strony: 121-131

Daty

wydano

2003

Twórcy

autor

Daniel Pellegrino

• Departamento de Matemática e Estatística, Caixa Postal 10044, Campina Grande, PB, Brazil, Cep 58109-970

Identyfikatory

DOI

10.4064/sm157-2-2