STRICTLY SINGULAR INCLUSIONS BETWEEN SYMMETRIC SEQUENCE SPACES.

VÍCTOR MANUEL SÁNCHEZ DE LOS REYES.

Joint work with F.L. Hernández and E.M. Semenov

Abstract: Strict singularity of inclusions between symmetric sequence spaces will be studied. Suitable conditions will be provided involving the associated fundamental functions. The special case of Lorentz and Marcinkiewicz spaces will be characterized. It will be also showed that if E ↪ F are symmetric sequence spaces with E ≠ ℓ_{1} and F ≠ c_{0} and ℓ_{∞} then there exist a intermediate symmetric sequence space G such that E ↪ G ↪ F and both inclusions are not strictly singular. As a consequence new characterizations of the spaces c_{0} and ℓ_{1} inside the class of all symmetric sequence spaces will be given.

Departamento de Análisis Matemático. Universidad Complutense de Madrid. 28040 Madrid, SPAIN