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.

Examples and non-examples

• $c_{0}$ the space of convergent sequences with the supremum norm has the AK property.
• $\ell ^{p}$ ($1\leq p<\infty$) the absolutely p-summable sequences with the $\|\cdot \|_{p}$ norm have the AK property.
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \ell^\infty} with the supremum norm does not have the AK property.

Properties

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

FK-AK spaces are separable spaces.

See also

• 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