In mathematics, specifically in order theory and functional analysis, a band in a vector lattice
[1] The smallest band containing a subset
is called the band generated by
[1] A band generated by a singleton set is called a principal band.
of a vector lattice
the set
disjoint from
is a band in
) is the usual space of real valued functions used to define Lp spaces
is countably order complete (that is, each subset that is bounded above has a supremum) but in general is not order complete.
is the vector subspace of all
is a solid subset of
that is not a band.
[1] The intersection of an arbitrary family of bands in a vector lattice
is a band in