FK-AK space

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.

• ${\displaystyle c_{0}}${\displaystyle c_{0}} the space of convergent sequences with the supremum norm has the AK property.
• ${\displaystyle \ell ^{p}}${\displaystyle \ell ^{p}} (${\displaystyle 1\leq p<\infty }${\displaystyle 1\leq p<\infty }) the absolutely p-summable sequences with the ${\displaystyle \|\cdot \|_{p}}${\displaystyle \|\cdot \|_{p}} norm have the AK property.
• ${\displaystyle \ell ^{\infty }}${\displaystyle \ell ^{\infty }} with the supremum norm does not have the AK property.

An FK-AK space ${\displaystyle E}${\displaystyle E} has the property $${\displaystyle E'\simeq E^{\beta }}$${\displaystyle E'\simeq E^{\beta }} that is the continuous dual of ${\displaystyle E}${\displaystyle E} is linear isomorphic to the beta dual of ${\displaystyle E.}${\displaystyle E.}

FK-AK spaces are separable spaces.

• BK-space – Sequence space that is Banach
• FK-space – Sequence space that is Fréchet
• Normed space – Vector space on which a distance is definedPages displaying short descriptions of redirect targets
• Sequence space – Vector space of infinite sequences

• Topological vector spaces
• Linear algebra stubs

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