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When is the Haar measure a Pietsch measure for nonlinear mappings? (English) Zbl 1276.28028
Authors’ 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 \(C(G)\). We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section, some problems are proposed.”
One of the open problems reads as follows.
Let \(F\) be a closed translation invariant subspace of \(C(G)\), let \(X\) be a metric space and \(f: F\to X\) be a translation invariant Lipschitz \(p\)-summing mapping. Is the Haar measure a Pietsch measure for \(f\)?

MSC:
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
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