Trisha Shetty (Editor)

K space (functional analysis)

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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 → R → X → V → 0.

is equivalent to the trivial one

0 → R → R × V → V → 0.

where R is the real line.

Examples

  • Finite dimensional Banach spaces are K-spaces.
  • The ℓ p spaces for 0 < p < 1 are K-spaces.
  • N. J. Kalton and N. P. Roberts proved that the Banach space ℓ 1 is not a K-space.

    • References

    K-space (functional analysis) Wikipedia
    (Text) CC BY-SA