Compactness properties of bounded subsets of spaces of vector measure integrable functions and factorization of operators
Submitted: 2013-11-25
|Accepted: 2013-11-25
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Keywords:
Compactness, Vector measures, Integration, Factorization
Supporting agencies:
Generalitat Valenciana
Spain
grant GV04B-371
the Spanish Ministry of Science and Technology
Plan Nacional I D I
grant BFM2003-02302
and the Universidad Politécnica de Valencia
under grant 2003-4114 for Interdisciplinary Research Projects.
Abstract:
Using compactness properties of bounded subsets of spaces of vector measure integrable functions and a representation theorem for q-convex Banach lattices, we prove a domination theorem for operators between Banach lattices. We generalize in this way several classical factorization results for operators between these spaces, as psumming operators.
References:
G. P. Curbera, Operators into L1 of a vector measure and applications to Banach lattices, Math. Ann. 293 (1992), 317-330. https://doi.org/10.1007/BF01444717
G. P. Curbera, Banach space properties of L1 of a vector measure, Proc. Amer. Math. Soc. 123 (1995), 3797-3806. https://doi.org/10.2307/2161909
A. Defant, Variants of the Maurey-Rosenthal theorem for quasi Köthe function spaces, Positivity 5 (2001), 153-175. https://doi.org/10.1023/A:1011466509838
A. Defant and K. Floret, "Tensor Norms and Operator Ideals", North Holland, Amsterdam (1993).
J. Diestel, H. Jarchow and A. Tonge, "Absolutely Summing Operators", Cambridge studies in advanced mathematics 43, Cambridge (1995). https://doi.org/10.1017/CBO9780511526138
J. Diestel and J. J. Uhl, Vector Measures, Math. Surveys, 15, Amer. Math. Soc., Providence, RI. 1977. https://doi.org/10.1090/surv/015
A. Fernández, F. Mayoral, F. Naranjo, F. Sáez and E. A. Sánchez-Pérez, Spaces of p-integrable functions with respect to a vector measure, Positivity, to appear.
J. Lindenstrauss and L. Tzafriri, "Classical Banach Spaces I and II", Springer, Berlin (1996). https://doi.org/10.1007/978-3-540-37732-0
F. Martínez-Giménez and E. A. Sánchez-Pérez, Vector measure range duality and factorizations of (D, p)-summing operators from Banach function spaces, Bull. Braz. Math. Soc., New Series 35(1)(2004), 51-69. https://doi.org/10.1007/s00574-004-0003-1
S. Okada and W. J. Ricker, The range of the integration map of a vector measure, Arch. Math. 64(1995), 512-522. https://doi.org/10.1007/BF01195133
S. Okada, W. J. Ricker and L. Rodríguez-Piazza, Compactness of the integration operator associated with a vector measure, Studia Math. 150(2) (2002), 133-149. https://doi.org/10.4064/sm150-2-3
A. Pietsch, "Operator Ideals", North-Holland, Amsterdam (1980).
E. A. Sánchez-Pérez, Compactness arguments for spaces of p-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces, Illinois J. Math. 45(3) (2001), 907-923. https://doi.org/10.1215/ijm/1258138159
E. A. Sánchez-Pérez, Spaces of integrable functions with respect to vector measures of convex range and factorization of operators from Lp-spaces, Pacific J. Math. 207 (2) (2002), 489-495. https://doi.org/10.2140/pjm.2002.207.489
P. Wojtaszczyk, "Banach Spaces for Analysts", Cambridge University Press. Cambridge. 1991. https://doi.org/10.1017/CBO9780511608735
