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. Definition Given a sequence space the -dual of is defined as If is an FK-space then each in defines a continuous linear form on Examples Properties 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. Functional analysis