Template:Functional analysis

v t e Functional analysis (topics)
Spaces	Hilbert space, Banach space, Fréchet space, topological vector space
Theorems	Hahn–Banach theorem, closed graph theorem, uniform boundedness principle, Kakutani fixed-point theorem, min-max theorem, Gelfand–Naimark theorem, Banach–Alaoglu theorem
Operators	bounded operator, compact operator, adjoint operator, unitary operator, Hilbert–Schmidt operator, trace class, unbounded operator
Algebras	Banach algebra, C-algebra, spectrum of a C-algebra, operator algebra, group algebra of a locally compact group
Open problems	invariant subspace problem, Mahler's conjecture
Applications	Besov space, Hardy space, spectral theory of ordinary differential equations, heat kernel, index theorem, calculus of variation, functional calculus
Advanced topics	locally convex space, approximation property, balanced set, Schwartz space, weak topology, barrelled space, Banach–Mazur distance