Normed vector lattice


In mathematics, specifically in order theory and functional analysis, a normed lattice is a topological vector lattice that is also a normed space space whose unit ball is a solid set.
Normed lattices are important in the theory of topological vector lattices.

Properties

Every normed lattice is a locally convex vector lattice.
The strong dual of a normed lattice is a Banach lattice with respect to the dual norm and canonical order.
If it is also a Banach space then its continuous dual space is equal to its order dual.

Examples

Every Banach lattice is a normed lattice.