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
- <math>c_0</math> the space of convergent sequences with the supremum norm has the AK property.
- <math>\ell^p</math> (<math>1 \leq p < \infty</math>) the absolutely p-summable sequences with the <math>\|\cdot\|_p</math> norm have the AK property.
- <math>\ell^\infty</math> with the supremum norm does not have the AK property.
Properties
An FK-AK space <math>E</math> has the property
<math display=block>E' \simeq E^\beta</math>
that is the continuous dual of <math>E</math> is linear isomorphic to the beta dual of <math>E.</math>
FK-AK spaces are separable spaces.