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- Title
POSITIVELY NORMING SETS IN BANACH FUNCTION SPACES.
- Authors
Pérez, E. A. Sánchez; Tradacete, P.
- 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 L1-spaces. As an application, we provide a version of Kadec–Pełczyński's dichotomy for order continuous Banach function spaces. A general description of positively norming sets using vector measure integration is also given.
- Subjects
BANACH spaces; FUNCTION spaces; EMBEDDINGS (Mathematics); SUBSPACES (Mathematics); ISOMORPHISM (Mathematics); INTEGRABLE functions
- Publication
Quarterly Journal of Mathematics, 2014, Vol 65, Issue 3, p1049
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hat035