FK-AK space
Encyclopedia
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
.
that is the continuous dual of E is linear isomorphic to the beta dual of E.
FK-AK spaces are separable
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
and related areas of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
an FK-AK space or FK-space
FK-space
In functional analysis and related areas of mathematics a FK-space or Fréchet coordinate space is a sequence space equipped with a topological structure such that it becomes a Fréchet space. FK-spaces with a normable topology are called BK-spaces....
with the AK property is an FK-space which contains the space of finite sequences and has a Schauder basis
Schauder basis
In mathematics, a Schauder basis or countable basis is similar to the usual basis of a vector space; the difference is that Hamel bases use linear combinations that are finite sums, while for Schauder bases they may be infinite sums...
.
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 E has the propertythat is the continuous dual of E is linear isomorphic to the beta dual of E.
FK-AK spaces are separable