# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Cotype and absolutely summing homogeneous polynomials in ${\cal L}_{p}$ spaces

### Tom 157 / 2003

Studia Mathematica 157(2003), 121-131 MSC: Primary 46B15; Secondary 46G25. DOI: 10.4064/sm157-2-2 Opublikowany online: 1 January 1970

#### Streszczenie

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.

#### Autorzy

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

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