This is a list of functional analysis topics.

See also: Glossary of functional analysis.

Hilbert space

Functional analysis, classic results

Operator theoryOperator theory

Banach space examples

• Lp space

• Hardy space

• Sobolev space

• Tsirelson space

• ba space

Real and complex associative algebraalgebrass

Topological vector spaceTopological vector spaces

Amenability

• Amenable group

• Von Neumann conjecture

WaveletWavelets

Quantum theory

See also list of mathematical topics in quantum theory

ProbabilityProbability

• 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