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