Daniel Pellegrino, Joedson Santos
Published 2010-04-15, updated 2010-10-22Version 3
The main goal of this paper is to characterize arbitrary nonlinear (non-multilinear) mappings $f:X_{1}\times...\times X_{n}\rightarrow Y$ between Banach spaces that satisfy a quite natural Pietsch Domination-type theorem around a given point $(a_{1},...,a_{n})\in$ $X_{1}\times...\times X_{n}$. As a consequence of our approach a notion of weighted summability arises naturally, which may be an interesting topic for further investigation.
Comments: This new presentation of the manuscript (quite modified and reduced) is the version accepted for publication in Math. Z. Part of the old version (which does not appear in this new version) will appear in a forthcoming paper
Classification of Banach Spaces --its Topological and Cardinality Properties
On complemented subspaces of sums and products of Banach spaces
The non-linear geometry of Banach spaces after Nigel Kalton
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