Quotient Banach Lattices Under Unbounded Norm Topology

Abstract

In this paper, we verify some extra properties in quotient Banach lattices. Especially, we characterize the zero neighborhoods under unbounded norm topology (un-topology) in quotient Banach lattices. We verify some types of convergence in a quotient Banach lattice. Also, we show that if a Banach lattice is atomic, then the quotient Banach lattice so is. Finally, we show that the quotient preserves Schur and Banach-Saks properties.

Keywords

• quotient banach lattice
• un-topology
• atom