Abstract
Let \(X(\mu )\) be a p-convex (\(1\le p<\infty \)) order continuous Banach function space over a positive finite measure \(\mu \). We characterize the subspaces of \(X(\mu )\) which can be found simultaneously in \(X(\mu )\) and a suitable \(L^1(\eta )\) space, where \(\eta \) is a positive finite measure related to the representation of \(X(\mu )\) as an \(L^p(m)\) space of a vector measure \(m\). We provide in this way new tools to analyze the strict singularity of the inclusion of \(X(\mu )\) in such an \(L^1\) space. No rearrangement invariant type restrictions on \(X(\mu )\) are required.
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J.M. Calabuig was supported by Ministerio de Economía y Competitividad (project MTM2011-23164) (Spain). J. Rodríguez was supported by Ministerio de Economía y Competitividad (project MTM2011-25377) (Spain). E.A. Sánchez-Pérez was supported by Ministerio de Economía y Competitividad (project MTM2009-14483-C02-02) (Spain)
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Calabuig, J.M., Rodríguez, J. & Sánchez-Pérez, E.A. Strongly embedded subspaces of p-convex Banach function spaces. Positivity 17, 775–791 (2013). https://doi.org/10.1007/s11117-012-0204-6
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DOI: https://doi.org/10.1007/s11117-012-0204-6
Keywords
- Strongly embedded subspace
- \(p\)-Convex Banach function space
- Strictly singular operator
- Vector measure