Beta-dual space

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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[edit]

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

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

Examples[edit]

Properties[edit]

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.