Banach space

Definitions

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.

error-lua-exec

Equivalents

Examples

“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.”

CEFR level