Geodesic
When is the Haar measure a Pietsch measure for nonlinear mappings?
Geraldo Botelho1 ; Daniel Pellegrino2 ; Pilar Rueda3 ; Joedson Santos4 ; Juan Benigno Seoane-Sepúlveda5
1 Faculdade de Matemática Universidade Federal de Uberlândia 38.400-902 Uberlândia, Brazil
2 Departamento de Matemática Universidade Federal da Paraíba 58.051-900 João Pessoa, Brazil
3 Departamento de Análisis Matemático Universidad de Valencia 46100 Burjasot, Valencia, Spain
4 Departamento de Matemática Universidade Federal de Sergipe 49.500-000 Itabaiana, Brazil
5 Departamento de Análisis Matemático Facultad de Ciencias Matemáticas Universidad Complutense de Madrid Plaza de Ciencias 3 28040 Madrid, Spain
Studia Mathematica, Tome 213 (2012) no. 3, pp. 275-287 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm213-3-5
Keywords: linear normalized haar measure compact topological group pietsch measure nonlinear summing mappings closed translation invariant subspaces answers question posed authors diestel result applies several well studied classes nonlinear summing mappings final section problems proposed

Geraldo Botelho 1 ; Daniel Pellegrino 2 ; Pilar Rueda 3 ; Joedson Santos 4 ; Juan Benigno Seoane-Sepúlveda 5

1 Faculdade de Matemática Universidade Federal de Uberlândia 38.400-902 Uberlândia, Brazil
2 Departamento de Matemática Universidade Federal da Paraíba 58.051-900 João Pessoa, Brazil
3 Departamento de Análisis Matemático Universidad de Valencia 46100 Burjasot, Valencia, Spain
4 Departamento de Matemática Universidade Federal de Sergipe 49.500-000 Itabaiana, Brazil
5 Departamento de Análisis Matemático Facultad de Ciencias Matemáticas Universidad Complutense de Madrid Plaza de Ciencias 3 28040 Madrid, Spain 
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     title = {When is the {Haar} measure a {Pietsch} measure
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     journal = {Studia Mathematica},
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     doi = {10.4064/sm213-3-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm213-3-5/}
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Geraldo Botelho; Daniel Pellegrino; Pilar Rueda; Joedson Santos; Juan Benigno Seoane-Sepúlveda. When is the Haar measure a Pietsch measure
 for nonlinear mappings?. Studia Mathematica, Tome 213 (2012) no. 3, pp. 275-287. doi: 10.4064/sm213-3-5

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