Banach space

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English[edit]

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Etymology[edit]

After Polish mathematician Stefan Banach (1892–1945).

Noun[edit]

Banach space (plural Banach spaces)

  1. (functional analysis) A normed vector space which is complete with respect to the norm, meaning that Cauchy sequences have well-defined limits that are points in the space.
    • 1962 [Prentice-Hall], Kenneth Hoffman, Banach Spaces of Analytic Functions, 2007, Dover, page 138,
      Before taking up the extreme points for and , let us make a few elementary observations about the unit ball in the Banach space .
    • 1992, R. M. Dudley, M. G. Hahn, James Kuelbs (editors), Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference, Springer, page ix,
      Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonseparable.
    • 2013, R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, American Mathematical Society, page 35,
      [A] Banach space is a complete normed linear space . Its dual space is the linear space of all continuous linear functionals , and it has norm ; is also a Banach space.

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