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
- 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
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Topological vector spaces (TVSs)
- Anderson–Kadec
- Banach–Alaoglu
- Closed graph theorem
- F. Riesz's
- Hahn–Banach (hyperplane separation
- Vector-valued Hahn–Banach)
- Open mapping (Banach–Schauder)
- Uniform boundedness (Banach–Steinhaus)
- Absolutely convex/disk
- Absorbing/Radial
- Affine
- Balanced/Circled
- Banach disks
- Bounding points
- Bounded
- Complemented subspace
- Convex
- Convex cone (subset)
- Linear cone (subset)
- Extreme point
- Pre-compact/Totally bounded
- Prevalent/Shy
- Radial
- Radially convex/Star-shaped
- Symmetric
- Asplund
- B-complete/Ptak
- Banach
- (Countably) Barrelled
- BK-space
- (Ultra-) Bornological
- Brauner
- Complete
- Convenient
- (DF)-space
- Distinguished
- F-space
- FK-AK space
- FK-space
- Fréchet
- Grothendieck
- Hilbert
- Infrabarreled
- Interpolation space
- K-space
- LB-space
- LF-space
- Locally convex space
- Mackey
- (Pseudo)Metrizable
- Montel
- Quasibarrelled
- Quasi-complete
- Quasinormed
- (Polynomially
- Semi-) Reflexive
- Riesz
- Schwartz
- Semi-complete
- Smith
- Stereotype
- (B
- Strictly
- Uniformly) convex
- (Quasi-) Ultrabarrelled
- Uniformly smooth
- Webbed
- With the approximation property
- Category
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