This is a list of functional analysis topics.

See also: Glossary of functional analysis.

• Lp space
• Hardy space
• Sobolev space
• Tsirelson space
• ba space

• Amenable group
• Von Neumann conjecture

See also list of mathematical topics in quantum theory

• Free probability
• Bernstein's theorem

• Fixed-point theorems in infinite-dimensional spaces

• 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