The Grothendieck-Pietsch domination principle for nonlinear summing integral operators
Studia Mathematica, Tome 129 (1998) no. 2, pp. 97-112
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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{10_4064_sm_129_2_97_112,
author = {Karl Lermer},
title = {The {Grothendieck-Pietsch} domination principle for nonlinear summing integral operators},
journal = {Studia Mathematica},
pages = {97--112},
publisher = {mathdoc},
volume = {129},
number = {2},
year = {1998},
doi = {10.4064/sm-129-2-97-112},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-129-2-97-112/}
}
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Karl Lermer. The Grothendieck-Pietsch domination principle for nonlinear summing integral operators. Studia Mathematica, Tome 129 (1998) no. 2, pp. 97-112. doi: 10.4064/sm-129-2-97-112
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