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Spaces of \(p\)-integrable functions with respect to a vector measure defined on a \(\delta \)-ring. (English) Zbl 1257.46019

Summary: We study the lattice properties of the Banach lattices \(L^p(\nu )\) and \(L_w^p(\nu )\) of \(p\)-integrable real-valued functions and weakly \(p\)-integrable real-valued functions with respect to a vector measure \(\nu \) defined on a \(\delta \)-ring. The relation between these two spaces, the study of the continuity and some kind of compactness properties of certain multiplication operators between different spaces \(L_p\) and/or \(L_w^q\) and the representation theorems of general Banach lattices via these spaces play a fundamental role.

MSC:

46G10 Vector-valued measures and integration
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B42 Banach lattices
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