Joedson Santos

Absolutely summing multilinear operators: a panorama

Abstract This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective search of “perfect” multilinear extensions of the ideal of absolutely summing operators. The final sections contain some open problems that may indicate lines for future investigation.

When is the Haar measure a Pietsch measure for nonlinear mappings

We show that, as in the linear case, the normalized Haar measure on a compact topological group

Some techniques on nonlinear analysis and applications

G

A general Pietsch Domination Theorem

is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of

ON SUMMABILITY OF NONLINEAR MAPPINGS: A NEW APPROACH

C(G)

A general Extrapolation Theorem for absolutely summing operators

. 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.