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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.
Examples and non-examples
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
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
- 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
References
Topological vector spaces (TVSs) | |
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Basic concepts | |
Main results | |
Maps | |
Types of sets | |
Set operations | |
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Spaces |
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Operators | |||||
Algebras | |||||
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