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K-space (functional analysis)

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In mathematics, more specifically in functional analysis, a K-space is an F-space such that every extension of F-spaces (or twisted sum) of the form is equivalent to the trivial one[1] where is the real line.

Examples

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The spaces for are K-spaces,[1] as are all finite dimensional Banach spaces.

N. J. Kalton and N. P. Roberts proved that the Banach space is not a K-space.[1]

See also

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References

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  1. ^ a b c Kalton, 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