Beta-dual Space
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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 X the ?-dual of X is defined as

If X is an FK-space then each y in X? 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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