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Mathematische Zeitschrift

, Volume 258, Issue 1, pp 87–106 | Cite as

Strictly singular inclusions into \(L^1 + L^\infty\)

  • Francisco L. Hernández
  • Víctor M. Sánchez
  • Evgeny M. SemenovEmail author
Article

Abstract

It is given a complete characterization of the strict singularity and the disjoint strict singularity of the inclusions EL 1 + L for the class of rearrangement invariant function spaces E on the \([0,\infty)\) interval. Their relationship is also analyzed. Suitable criteria are given involving the scale of order continuous weak L p -spaces for \(1 < p < \infty\) .

Keywords

Rearrangement invariant spaces Strict singularity Disjoint strict singularity Weak compactness 

Mathematics Subject Classification (2000)

46E30 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Francisco L. Hernández
    • 1
  • Víctor M. Sánchez
    • 1
  • Evgeny M. Semenov
    • 2
    Email author
  1. 1.Department of Mathematical Analysis, Faculty of MathematicsComplutense UniversityMadridSpain
  2. 2.Department of MathematicsVoronezh State UniversityVoronezhRussia

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