Order summable
In mathematics, specifically in order theory and functional analysis, a sequence of positive elements in a preordered vector space (that is, for all ) is called order summable if exists in .[1] For any , we say that a sequence of positive elements of is of type if there exists some and some sequence in such that for all .[1]
The notion of order summable sequences is related to the completeness of the order topology.
See also
[edit]- Ordered topological vector space
- Order topology (functional analysis) – Topology of an ordered vector space
- Ordered vector space – Vector space with a partial order
- Vector lattice – Partially ordered vector space, ordered as a lattice
References
[edit]- ^ a b Schaefer & Wolff 1999, pp. 230–234.
Bibliography
[edit]- 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. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.