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Disjoint strict singularity of inclusions between rearrangement invariant spaces

Francisco L. Hernández; Víctor M. Sánchez; Evgueni M. Semenov — 2001

Studia Mathematica

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

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