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FK AK space

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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.

Contents

Examples and non-examples

  • c 0 the space of convergent sequences with the supremum norm has the AK property
  • l p ( 1 ≤ p < ∞ ) the absolutely p-summable sequences with the ∥ ⋅ ∥ p norm have the AK property
  • l ∞ with the supremum norm does not have the AK property

    • Properties

    An FK-AK space E has the property

    E ′ ≃ E β

    that is the continuous dual of E is linear isomorphic to the beta dual of E.

    FK-AK spaces are separable

    References

    FK-AK space Wikipedia
    (Text) CC BY-SA