Calabuig, J. M.; Juan, M. A.; Sánchez Pérez, E. A. Spaces of \(p\)-integrable functions with respect to a vector measure defined on a \(\delta \)-ring. (English) Zbl 1257.46019 Oper. Matrices 6, No. 2, 241-262 (2012). 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. Cited in 4 Documents 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 Keywords:Banach lattice; \(\delta \)-ring; vector measure; integration PDFBibTeX XMLCite \textit{J. M. Calabuig} et al., Oper. Matrices 6, No. 2, 241--262 (2012; Zbl 1257.46019) Full Text: DOI