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

Volume 157 / 2003

Daniel Pellegrino Studia Mathematica 157 (2003), 121-131 MSC: Primary 46B15; Secondary 46G25. DOI: 10.4064/sm157-2-2


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.


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

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