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Cotype and absolutely summing linear operators

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Abstract

New applications of cotype to the theory of absolutely summing linear operators between Banach spaces are proved in this paper. Among other consequences we extend/complement some classical results of Bennett (Duke Math J 44:603–639, 1977) on the existence of non-absolutely summing operators between ℓ p spaces and of Davis and Johnson (Stud Math 51:81–85, 1974) on the existence of compact non-absolutely summing linear operators. We also point out that some of our results are sharp.

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Authors and Affiliations

  1. Faculdade de Matemática, Universidade Federal de Uberlândia, Uberlândia, 38400-902, Brazil

    Geraldo Botelho

  2. Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, 58051-900, Brazil

    Daniel Pellegrino

  3. Departamento de Análisis Matemático, Universidad de Valencia, 46100, Burjasot, Valencia, Spain

    Pilar Rueda

Authors
  1. Geraldo Botelho
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  2. Daniel Pellegrino
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  3. Pilar Rueda
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Corresponding author

Correspondence to Daniel Pellegrino.

Additional information

Geraldo Botelho was supported by CNPq Grant 306981/2008-4. Daniel Pellegrino was supported by INCT-Matemática, CNPq Grants 620108/2008-8 (Ed. Casadinho), 471686/2008-5 (Ed. Universal) and 308084/2006-3. Pilar Rueda was supported by Ministerio de Ciencia e Innovación MTM2008-03211/MTM.

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Botelho, G., Pellegrino, D. & Rueda, P. Cotype and absolutely summing linear operators. Math. Z. 267, 1–7 (2011). https://doi.org/10.1007/s00209-009-0591-y

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  • DOI: https://doi.org/10.1007/s00209-009-0591-y

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