Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4623954 | Journal of Mathematical Analysis and Applications | 2006 | 22 Pages |
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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