Beta-dual space

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
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

Examples

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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.