Hahn–Banach theorem
Teorema de Hahn–Banach
- Date
- 1927-1929 · confidence high
- Place
- Vienna, Austria
- Credited to
- Hans Hahn (1927); generalised by Stefan Banach in Lwów, 1929
- Field
- Knowledge & symbols
What was discovered
A central theorem of functional analysis that allows bounded linear functionals defined on a subspace to be extended to the whole vector space, guaranteeing enough continuous functionals to study the dual space.
Hahn proved the real case in 1927; Banach independently generalised it in 1929 at the Lwów school of mathematics.
What it led to
- Modern theory of dual spaces
- The Hahn-Banach separation (hyperplane separation) theorem in convex geometry