# Beta-dual space

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.

## Definition

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

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

## Examples

## Properties

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.

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