FK-AK space

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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
[l^p (1 \leq p < \infty)] the absolutely p-summable sequences with the [\|\cdot\|_p] norm have the AK property
[l^\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

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