List of functional analysis topics

Banach space examples

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

Amenability

• Amenable group
• Von Neumann conjecture

Quantum theory

[Probability]

• Free probability
• Bernstein's theorem

Non-linear

• Fixed-point theorems in infinite-dimensional spaces

History

• Stefan Banach
• Hugo Steinhaus
• John von Neumann
• Alain Connes