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

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

Properties

An FK-AK space E has the property

${\displaystyle E'\simeq E^{\beta }}$

that is the continuous dual of E is linear isomorphic to the beta dual of E.

FK-AK spaces are separable.