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Domination of operators on function spaces

Published online by Cambridge University Press:  01 January 2009

A. DEFANT  and
E. A. SÁNCHEZ PÉREZ
A. DEFANT
Affiliation:
Institut für Mathematik, Fakultät V, Universität Oldenburg, D-26111 Oldenburg, Germany. e-mail: defant@mathematik.uni-oldenburg.de
E. A. SÁNCHEZ PÉREZ
Affiliation:
Instituto de Matemática Pura y Aplicada U.P.V. Universidad Politécnica de Valencia. 46071 Valencia, Spain. e-mail: easancpe@mat.upv.es
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Abstract

We prove a domination theorem for operators on Köthe function spaces by probability measures which includes both the Maurey–Rosenthal domination theorem and the Pisier domination theorem as special cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 1 , January 2009 , pp. 57 - 66
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

REFERENCES

[1]Defant, A.Variants of the Maurey–Rosenthal theorem for quasi Köthe function spaces. Positivity 5 (2001), 153–175.CrossRefGoogle Scholar
[2]Defant, A. and Sánchez–Pérez, E. A.Maurey–Rosenthal factorization of positive operators and convexity. Math. Anal. Appl. 297 (2004), 771–790.CrossRefGoogle Scholar
[3]Diestel, J., Jarchow, H. and Tonge, A.Absolutely Summing Operators. Cambridge Studies in Advanced Math. no. 43 (Cambridge 1995).CrossRefGoogle Scholar
[4]Kalton, N. J. and Montgomery–Smith, S. J.Set-functions and factorization. Arch. Math. 61 (1993), 183–200.CrossRefGoogle Scholar
[5]Lindenstrauss, J. and Tzafriri, L.Classical Banach Spaces I and II (Springer, 1996).CrossRefGoogle Scholar
[6]Maurey, B.Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les spaces L p. Asterisque 11 (1974).Google Scholar
[7]Pisier, G.Factorization of operators through L p,∞ or L p,1 and non-commutative generalizations. Math. Ann. 276 (1986), 105–136.CrossRefGoogle Scholar
[8]Rosenthal, H. P.On subspaces of L p. Ann. of Math. 97 (1973), 344–373.CrossRefGoogle Scholar