This is a list of functional analysis topics.
See also: Glossary of functional analysis.
Hilbert space
Functional analysis, classic results
Operator theory
Banach space examples
- Lp space
- Hardy space
- Sobolev space
- Tsirelson space
- ba space
Real and complex algebras
Topological vector spaces
Amenability
- Amenable group
- Von Neumann conjecture
Wavelets
Quantum theory
See also list of mathematical topics in quantum theory
Probability
- Free probability
- Bernstein's theorem
Non-linear
- Fixed-point theorems in infinite-dimensional spaces
History
- Stefan Banach (1892–1945)
- Hugo Steinhaus (1887–1972)
- John von Neumann (1903-1957)
- Alain Connes (born 1947)
- Earliest Known Uses of Some of the Words of Mathematics: Calculus & Analysis
- Earliest Known Uses of Some of the Words of Mathematics: Matrices and Linear Algebra