In functional analysis and related areas of mathematics, the beta-dual or -dual is a certain linear subspace of the algebraic dual of a sequence space.
Given a sequence space , the -dual of is defined as
Here, so that denotes either the real or complex scalar field.
If is an FK-space then each in defines a continuous linear form on
The beta-dual of an FK-space is a linear subspace of the continuous dual of . If is an FK-AK space then the beta dual is linear isomorphic to the continuous dual.