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

G. Botelho, D. Pellegrino, P. Rueda, J. Santos, J. B. Seoane-Sepúlveda

Published 2012-04-25Version 1

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.