Positively norming sets in Banach function spaces Articles uri icon

authors

  • SANCHEZ PEREZ, E. A.
  • TRADACETE PEREZ, PEDRO

publication date

  • September 2014

start page

  • 1049

end page

  • 1068

issue

  • 3

volume

  • 65

International Standard Serial Number (ISSN)

  • 0033-5606

Electronic International Standard Serial Number (EISSN)

  • 1464-3847

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-Pelczynski's dichotomy for order continuous Banach function spaces. A general description of positively norming sets using vector measure integration is also given.

keywords

  • lattices; operators; noncompactness; boundaries; theorem