When is the Haar measure a Pietsch measure for nonlinear mappings?
Volume 213 / 2012
Studia Mathematica 213 (2012), 275-287
MSC: Primary 28C10; Secondary 47B10.
DOI: 10.4064/sm213-3-5
Abstract
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.
