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Strongly embedded subspaces of p-convex Banach function spaces

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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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Authors and Affiliations

  1. Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 , Valencia, Spain

    J. M. Calabuig & E. A. Sánchez-Pérez

  2. Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100 , Espinardo (Murcia), Spain

    J. Rodríguez

Authors
  1. J. M. Calabuig
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  2. J. Rodríguez
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  3. E. A. Sánchez-Pérez
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Correspondence to J. Rodríguez.

Additional information

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

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