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

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  •   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

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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

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  • 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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