In functional analysis and related areas of mathematics, the beta-dual or β-dual is a certain linear subspace of the algebraic dual of a sequence space.

Given a sequence space X, the β-dual of X is defined as

Here, ${\displaystyle \mathbb {K} \in \{\mathbb {R} ,\mathbb {C} \}}$ so that ${\displaystyle \mathbb {K} }$ denotes either the real or complex scalar field.

If X is an FK-space then each y in X^β defines a continuous linear form on X

The beta-dual of an FK-space E is a linear subspace of the continuous dual of E. If E is an FK-AK space then the beta dual is linear isomorphic to the continuous dual.