A complete normed vector space (V, ‖·‖). Hahn–Banach, open mapping, closed graph, and uniform boundedness theorems form the four pillars of linear functional analysis on Banach spaces.
Banach space
Related concepts
- Real numbers (ℝ)
- Vector space
- Cauchy sequence
- Hilbert space
- Fréchet space
- Distributions (Schwartz)
- Hahn-Banach theorem
- Open mapping theorem
- Banach-Steinhaus (uniform boundedness)
- Fredholm operator
- Weak / weak-* convergence
- Strongly-continuous semigroups (C_0)
- Banach (1932)
- Hahn-Banach (1929)
- MOSFET square-law & short-channel
- Squeezed-vacuum injection: 3-dB shot-noise reduction below SQL in LIGO