FK-AK space
From HandWiki
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]\displaystyle{ c_0 }[/math] the space of convergent sequences with the supremum norm has the AK property
- [math]\displaystyle{ l^p (1 \leq p \lt \infty) }[/math] the absolutely p-summable sequences with the [math]\displaystyle{ \|\cdot\|_p }[/math] norm have the AK property
- [math]\displaystyle{ l^\infty }[/math] with the supremum norm does not have the AK property
Properties
An FK-AK space E has the property
- [math]\displaystyle{ E' \simeq E^\beta }[/math]
that is the continuous dual of E is linear isomorphic to the beta dual of E.
FK-AK spaces are separable.
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