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.
• ${\displaystyle \ell ^{p))$ (${\displaystyle 1\leq p<\infty }$) the absolutely p-summable sequences with the ${\displaystyle \|\cdot \|_{p))$ norm have the AK property.
• ${\displaystyle \ell ^{\infty ))$ with the supremum norm does not have the AK property.

Properties

An FK-AK space ${\displaystyle E}$ has the property

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

${\displaystyle E}$

${\displaystyle E.}$

FK-AK spaces are separable spaces.