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
• $l^{p}(1\leq p<\infty )$ 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