Some properties of weak Banach-Saks operators

Abstract

We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, {\rm L}-weakly compact; respectively, {\rm M}-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).

Keywords

• weak banach-saks operator
• weakly compact operator
• {\rm l}-weakly compact operator
• {\rm m}-weakly compact operator
• order continuous norm, positive schur property
• reflexive banach space