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.[1] Normed lattices are important in the theory of topological vector lattices.
Properties
Every normed lattice is a locally convex vector lattice.[1]
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.[1]
Examples
Every Banach lattice is a normed lattice.
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See also
- Banach lattice
- Fréchet lattice
- Locally convex vector lattice
- Vector lattice
References
- Schaefer & Wolff 1999, pp. 234–242.
- Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
- Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.CS1 maint: ref=harv (link)
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