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Strictly singular and strictly co-singular inclusions between symmetric sequence spaces

Hernández, Francisco L. and Sánchez de los Reyes, Víctor Manuel and Semenov, Evgeny M. (2004) Strictly singular and strictly co-singular inclusions between symmetric sequence spaces. Journal of Mathematical Analysis and Applications, 291 (2). pp. 459-476. ISSN 0022-247X

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Abstract

Strict singularity and strict co-singularity of inclusions between symmetric sequence spaces are studied. Suitable conditions are provided involving the associated fundamental functions. The special case of Lorentz and Marcinkiewicz spaces is characterized. It is also proved that if E hooked right arrow F are symmetric sequence spaces with E ≠ l(1) and F ≠ l c(0) and l(∞) then there exist a intermediate symmetric sequence space G such that E hooked right arrow G hooked right arrow F and both inclusions are not strictly singular. As a consequence new characterizations of the spaces c(o) and l(1) inside the class of all symmetric sequence spaces are given.


Item Type:Article
Uncontrolled Keywords:Basic sequences; Orlicz spaces; operators
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16004
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