Banach space

Noun

Banach space (plural Banach spaces)

1. (error-lua-exec, 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 H¹ and H ᪲, let us make a few elementary observations about the unit ball Σ in the Banach space X.
   • Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonseparable.1992, R. M. Dudley, M. G. Hahn, James Kuelbs, editors, Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference, Springer, page ix