Disjoint strict singularity of inclusions between rearrangement invariant spaces

Volume 144 / 2001

Francisco L. Hernández, Víctor M. Sánchez, Evgueni M. Semenov Studia Mathematica 144 (2001), 209-226 MSC: Primary 46E30. DOI: 10.4064/sm144-3-2

Abstract

It is studied when inclusions between rearrangement invariant function spaces on the interval $[0,\infty )$ are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions $L^1\cap L^\infty \hookrightarrow E$ and $E\hookrightarrow L^1+L^\infty $ to be disjointly strictly singular are shown. Applications to the classes of Lorentz and Marcinkiewicz spaces are given.

Authors

  • Francisco L. HernándezDepartament of Mathematical Analysis
    Faculty of Mathematics
    Complutense University
    28040 Madrid, Spain
    e-mail
  • Víctor M. SánchezDepartament of Mathematical Analysis
    Faculty of Mathematics
    Complutense University
    28040 Madrid, Spain
    e-mail
  • Evgueni M. SemenovDepartment of Mathematics
    Voronezh State University
    Voronezh 394693, Russia
    e-mail

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