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The history of a general criterium on spaceability

Víctor M. Sánchez — 2017

Open Mathematics

There are just a few general criteria on spaceability. This survey paper is the history of one of the first ones. Let I1 and I2 be arbitrary operator ideals and E and F be Banach spaces. The spaceability of the set of operators I1(E, F) I2(E, F) is studied. Before stating the criterium, the paper summarizes the main results about lineability and spaceability of differences between particular operator ideals obtained in recent years. They are the seed of the ideas contained in the general criterium....

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 ∩ L ∞ ↪ E and E ↪ L ¹ + L ∞ to be disjointly strictly singular are shown. Applications to the classes of Lorentz and Marcinkiewicz spaces are given.

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