List of functional analysis topics

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