Absolutely summing operators and integration of vector-valued functions |
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Authors: | José Rodríguez |
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Institution: | Departamento de Matemáticas, Universidad de Murcia, 30.100 Espinardo, Murcia, Spain |
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Abstract: | Let (Ω,Σ,μ) be a complete probability space and an absolutely summing operator between Banach spaces. We prove that for each Dunford integrable (i.e., scalarly integrable) function the composition u○f is scalarly equivalent to a Bochner integrable function. Such a composition is shown to be Bochner integrable in several cases, for instance, when f is properly measurable, Birkhoff integrable or McShane integrable, as well as when X is a subspace of an Asplund generated space or a subspace of a weakly Lindelöf space of the form C(K). We also study the continuity of the composition operator f?u○f. Some other applications are given. |
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Keywords: | Absolutely summing operator Dunford integral Pettis integral Bochner integral Birkhoff integral McShane integral Properly measurable function Non-separable Banach spaces |
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