We transform the concept of p-summing operators, 1≤ p < ∞, to the more general setting of nonlinear Banach space operators. For 1-summing operators on B(Σ,X)-spaces having weak integral representations we generalize the Grothendieck-Pietsch domination principle. This is applied for the characterization of 1-summing Hammerstein operators on C(S,X)-spaces. For p-summing Hammerstein operators we derive the existence of control measures and p-summing extensions to B(Σ,X)-spaces.
@article{bwmeta1.element.bwnjournal-article-smv129i2p97bwm,
author = {Karl Lermer},
title = {The Grothendieck-Pietsch domination principle for nonlinear summing integral operators},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {97-112},
zbl = {0911.47022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv129i2p97bwm}
}
Lermer, Karl. The Grothendieck-Pietsch domination principle for nonlinear summing integral operators. Studia Mathematica, Tome 129 (1998) pp. 97-112. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv129i2p97bwm/
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