Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced [ˈbanax]) is a complete normed vector space.

Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well defined limit that is within the space.

Description

Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly.

Banach spaces originally grew out of the study of function spaces by David Hilbert, Fréchet, and Riesz earlier in the century.

Banach spaces play a central role in functional analysis. In other areas of analysis, the spaces under study are often Banach spaces.

See also

• Complete metric space
• Distortion problem
• Functional analysis
• Interpolation space
• Normed vector space
• Space (mathematics)
  • Hilbert space
  • Lp space
  • Sobolev space
  • Hardy space

External links

• Banach space @ Wikipedia