In mathematics, specifically in order theory and functional analysis, the order bound dual of an ordered vector space
is the set of all linear functionals on
that map order intervals, which are sets of the form
[1] The order bound dual of
This space plays an important role in the theory of ordered topological vector spaces.
of the order bound dual of
The positive elements of the order bound dual form a cone that induces an ordering on
called the canonical ordering.
is an ordered vector space whose positive cone
) then the order bound dual with the canonical ordering is an ordered vector space.
[1] The order bound dual of an ordered vector spaces contains its order dual.
[1] If the positive cone of an ordered vector space
then the order dual is equal to the order bound dual, which is an order complete vector lattice under its canonical ordering.
are order bounded linear forms on