FK-AK space

In functional analysis and related areas of mathematics an FK-AK space or FK-space with the AK property is an FK-space which contains the space of finite sequences and has a Schauder basis.

Examples and non-examples

$c_{0}$ the space of convergent sequences with the supremum norm has the AK property.
$\ell ^{p}$ ( $1\leq p<\infty$ ) the absolutely p-summable sequences with the $\|\cdot \|_{p}$ norm have the AK property.
$\ell ^{\infty }$ with the supremum norm does not have the AK property.

Properties

An FK-AK space $E$ has the property $E'\simeq E^{\beta }$ that is the continuous dual of $E$ is linear isomorphic to the beta dual of $E.$

FK-AK spaces are separable spaces.

References

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Category

Examples and non-examples

Properties

See also

References