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.