When is the Haar measure a Pietsch measure for nonlinear mappings?

Volume 213 / 2012

Geraldo Botelho, Daniel Pellegrino, Pilar Rueda, Joedson Santos, Juan Benigno Seoane-Sepúlveda Studia Mathematica 213 (2012), 275-287 MSC: Primary 28C10; Secondary 47B10. DOI: 10.4064/sm213-3-5


We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed.


  • Geraldo BotelhoFaculdade de Matemática
    Universidade Federal de Uberlândia
    38.400-902 Uberlândia, Brazil
  • Daniel PellegrinoDepartamento de Matemática
    Universidade Federal da Paraíba
    58.051-900 João Pessoa, Brazil
  • Pilar RuedaDepartamento de Análisis Matemático
    Universidad de Valencia
    46100 Burjasot, Valencia, Spain
  • Joedson SantosDepartamento de Matemática
    Universidade Federal de Sergipe
    49.500-000 Itabaiana, Brazil
  • Juan Benigno Seoane-SepúlvedaDepartamento de Análisis Matemático
    Facultad de Ciencias Matemáticas
    Universidad Complutense de Madrid
    Plaza de Ciencias 3
    28040 Madrid, Spain

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