On summability of nonlinear mappings: a new approach

Details On summability of nonlinear mappings: a new approach On summability of nonlinear mappings: a new approach

2010-04-15

arxiv.org/abs/1004.2643v3

Mathematics

Functional Analysis

This new presentation of the manuscript (quite modified and reduced) is the version accepted for publication in Math. Z. Part

Scientific paper

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.

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