Order summable

In mathematics, specifically in order theory and functional analysis, a sequence of positive elements in a preordered vector space X (i.e. xi ≥ 0 for all i) is called order summable if exists in X.[1] For any , we say that a sequence of positive elements of X is of type if there exists some z in X and some sequence in such that for all i.[1]

The notion of order summable sequences is related to the completeness of the order topology.

See also

References

  1. Schaefer & Wolff 1999, pp. 230–234.

Bibliography

  • 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.
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