34 research outputs found
Absolutely summing multilinear operators: a panorama
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 \textquotedblleft perfect\textquotedblright \
multilinear extensions of the ideal of absolutely summing operators. The final
section contains some open problems that may indicate lines for future
investigation.Comment: 30 page
Some techniques on nonlinear analysis and applications
In this paper we present two different results in the context of nonlinear
analysis. The first one is essentially a nonlinear technique that, in view of
its strong generality, may be useful in different practical problems. The
second result, more technical, but also connected to the first one, is an
extension of the well-known Pietsch Domination Theorem. The last decade
witnessed the birth of different families of Pietsch Domination-type results
and some attempts of unification. Our result, that we call "full general
Pietsch Domination Theorem" is potentially a definitive Pietsch Domination
Theorem which unifies the previous versions and delimits what can be proved in
this line.The connections to the recent notion of weighted summability are
traced.Comment: 24 page
A general Extraplolation Theorem for absolutely summing operators
In this note we prove a general version of the Extrapolation Theorem,
extending the classical linear extrapolation theorem due to B. Maurey. Our
result shows, in particular, that the operators involved do not need to be
linear