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    Banach Space

    Description

    A vector space that possesses a norm which allows computation of vector length and distance between vectors and that is complete in the sense that Cauchy sequences converge.

    Relationship graph

    Relationship graph

    More general classifications

    Baire space | barrelled space | bornological space | compactly generated space | complete space | convenient space | Fréchet space | F-space | locally complete space | locally convex space | Mackey space | metrizable space | normed space | pseudo-complete space | pseudo-metrizable space | quasi-Banach space | quasi-barrelled space | quasi-complete space | quasi-normed space | seminormed space | sequentially complete space | stereotype space | topological vector space | webbed space

    Examples

    A^1(D, dλ^2) | A^2(D, dλ^2) | ℬ(D, dλ^2) | L^∞(T;X) | a^1(D, dλ^2) | a^2(D, dλ^2) | ℬ^h(D, dλ^2) | h^2 | h^∞ | ℬ_0^h(D, dλ^2) | H^2 | H^∞ | L^2(D, dλ^2) | L^∞(D, dλ^2) | ℬ_0(D, dλ^2) | c_0(Z^+, dη) | ℓ^2(Z^+, dη) | ℓ^∞(Z^+, dη)

    History

    1920 to 1922

    Stefan Banach (mathematician)

    Hans Hahn | Eduard Helly

    Timeline

    Timeline

    References

    Gustave Choquet. Lectures on Analysis. Vol. I: Integration and Topological Vector Spaces. p. 25, 1969. Paul Garrett.

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