Login
Login

K-space (functional analysis)

In mathematics, more specifically in functional analysis, a K-space is an F-space V such that every extension of F-spaces (or twisted sum) of the form

0 \rightarrow \R \rightarrow X \rightarrow V \rightarrow 0. \,\!

is equivalent to the trivial oneKalton, N. J.; Peck, N. T.; Roberts, James W. An F-space sampler. London Mathematical Society Lecture Note Series, 89. Cambridge University Press, Cambridge, 1984. xii+240 pp. {{isbn|0-521-27585-7}}

0\rightarrow \R \rightarrow \R \times V \rightarrow V \rightarrow 0. \,\!

where \R is the real line.

Examples

The \ell^p spaces for 0< p < 1 are K-spaces, as are all finite dimensional Banach spaces.

N. J. Kalton and N. P. Roberts proved that the Banach space \ell^1 is not a K-space.

See also

  • {{annotated link|Compactly generated space}}
  • {{annotated link|Gelfand–Shilov space}}

References

{{reflist|group=note}}

{{reflist}}

{{Functional analysis}}

{{Topological vector spaces}}

Category:Functional analysis

Category:F-spaces

Category:Topological vector spaces