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
[edit]- the space of convergent sequences with the supremum norm has the AK property.
- () the absolutely p-summable sequences with the norm have the AK property.
- with the supremum norm does not have the AK property.
Properties
[edit]An FK-AK space has the property that is the continuous dual of is linear isomorphic to the beta dual of
FK-AK spaces are separable spaces.
See also
[edit]- BK-space – Sequence space that is Banach
- FK-space – Sequence space that is Fréchet
- Normed space – Vector space on which a distance is defined
- Sequence space – Vector space of infinite sequences
References
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