Positively norming sets in Banach function spaces

Autores UPV
Año
Revista QUARTERLY JOURNAL OF MATHEMATICS

Abstract

The notion of positively norming set, a specific definition of norming type sets for Banach lattices, is analyzed. We show that the size of positively norming sets (in terms of compactness and order boundedness) is directly related to the existence of lattice copies of L 1-spaces. As an application, we provide a version of Kadec¿Pelczinski's dichotomy for order continuous Banach function spaces. A general description of positively norming sets using vector measure integration is also given.