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

Tom 213 / 2012

Studia Mathematica 213 (2012), 275-287 MSC: Primary 28C10; Secondary 47B10. DOI: 10.4064/sm213-3-5

Streszczenie

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.

Autorzy

38.400-902 Uberlândia, Brazil
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• Daniel PellegrinoDepartamento de Matemática
58.051-900 João Pessoa, Brazil
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• Pilar RuedaDepartamento de Análisis Matemático
46100 Burjasot, Valencia, Spain
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• Joedson SantosDepartamento de Matemática
49.500-000 Itabaiana, Brazil
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• Juan Benigno Seoane-SepúlvedaDepartamento de Análisis Matemático