# The Grothendieck-Pietsch domination principle for nonlinear summing integral operators

Studia Mathematica (1998)

- Volume: 129, Issue: 2, page 97-112
- ISSN: 0039-3223

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topLermer, Karl. "The Grothendieck-Pietsch domination principle for nonlinear summing integral operators." Studia Mathematica 129.2 (1998): 97-112. <http://eudml.org/doc/216499>.

@article{Lermer1998,

abstract = {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.},

author = {Lermer, Karl},

journal = {Studia Mathematica},

keywords = {-summing operators; nonlinear Banach space operators; Grothendieck-Pietsch domination principle; 1-summing Hammerstein operators; control measures; -summing extensions},

language = {eng},

number = {2},

pages = {97-112},

title = {The Grothendieck-Pietsch domination principle for nonlinear summing integral operators},

url = {http://eudml.org/doc/216499},

volume = {129},

year = {1998},

}

TY - JOUR

AU - Lermer, Karl

TI - The Grothendieck-Pietsch domination principle for nonlinear summing integral operators

JO - Studia Mathematica

PY - 1998

VL - 129

IS - 2

SP - 97

EP - 112

AB - 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.

LA - eng

KW - -summing operators; nonlinear Banach space operators; Grothendieck-Pietsch domination principle; 1-summing Hammerstein operators; control measures; -summing extensions

UR - http://eudml.org/doc/216499

ER -

## References

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- [5] J. Diestel, Sequences and Series in Banach Spaces, Springer, Berlin, 1984.
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- [7] N. Dinculeanu, Vector Measures, Pergamon Press, Oxford, 1967.
- [8] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
- [9] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1981. Zbl0466.46001
- [10] K. Lermer, Characterizations of weakly compact nonlinear integral operators on C(S)-spaces, Stud. Cerc. Mat. 48 (1996), 365-378. Zbl0859.47035
- [11] A. Pietsch, Operator Ideals, North-Holland, 1980.

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