Geodesic
Cotype and absolutely summing homogeneous polynomials in ${\cal L}_{p}$ spaces
Daniel Pellegrino1
1 Departamento de Matemática e Estatística Caixa Postal 10044 Campina Grande, PB, Brazil Cep 58109-970
Studia Mathematica, Tome 157 (2003) no. 2, pp. 121-131

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 ${\cal L}_{\infty }$ spaces.
DOI : 10.4064/sm157-2-2
Keywords: lift homogeneous polynomials multilinear mappings linear result due lindenstrauss czy ski absolutely summing operators explore notion cotype obtain stronger results provide various examples situations which space absolutely summing homogeneous polynomials different whole space homogeneous polynomials among other consequences these results enable obtain answers questions about absolutely summing homogeneous polynomials multilinear mappings cal infty spaces

Daniel Pellegrino 1

1 Departamento de Matemática e Estatística Caixa Postal 10044 Campina Grande, PB, Brazil Cep 58109-970 
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Daniel Pellegrino. Cotype and absolutely summing homogeneous
  polynomials in ${\cal L}_{p}$ spaces. Studia Mathematica, Tome 157 (2003) no. 2, pp. 121-131. doi: 10.4064/sm157-2-2

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