Template:Functional analysis
Spaces
Properties
barrelled
complete
dual (algebraic/topological)
locally convex
reflexive
separable
Theorems
Hahn–Banach
Riesz representation
closed graph
uniform boundedness principle
Kakutani fixed-point
Krein–Milman
min–max
Gelfand–Naimark
Banach–Alaoglu
Operators
adjoint
bounded
compact
Hilbert–Schmidt
normal
nuclear
trace class
transpose
unbounded
unitary
Algebras
Banach algebra
C*-algebra
spectrum of a C*-algebra
operator algebra
group algebra of a locally compact group
von Neumann algebra
Open problems
invariant subspace problem
Mahler's conjecture
Applications
Hardy space
spectral theory of ordinary differential equations
heat kernel
index theorem
calculus of variations
functional calculus
integral operator
Jones polynomial
topological quantum field theory
noncommutative geometry
Riemann hypothesis
distribution (or generalized functions)
Advanced topics
approximation property
balanced set
Choquet theory
weak topology
Banach–Mazur distance
Tomita–Takesaki theory
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