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