((Navbox
| name = Functional analysis
| title = [[Functional analysis]]&nbsp;([[List of functional analysis topics|topics]] – [[Glossary of functional analysis|glossary]])
| bodyclass  = hlist
| state      = (({state|))}

| group1     = Spaces
| list1      = 
  ((Navbox|subgroup
  | group1 =
  | list1  =
*[[Banach space|Banach]] 
*[[Besov space|Besov]] 
*[[Fréchet space|Fréchet]] 
*[[Hilbert space|Hilbert]]
*[[Hölder space|Hölder]]
*[[Nuclear space|Nuclear]]
*[[Orlicz space|Orlicz]]
*[[Schwartz space|Schwartz]]
*[[Sobolev space|Sobolev]]
*[[Topological vector space|Topological vector]]
  | group2 = Properties
  | list2  =
*[[Barrelled space|Barrelled]]
*[[Complete topological vector space|Complete]]
*[[Dual space|Dual]] ([[Dual space#Algebraic dual space|Algebraic]]/[[Dual space#Continuous dual space|Topological]])
*[[Locally convex topological vector space|Locally convex]] 
*[[Reflexive space|Reflexive]]
*[[Separable space|Separable]]
 ))

| group2     = [[:Category:Theorems in functional analysis|Theorems]]
| list2      = 
*[[Hahn–Banach theorem|Hahn–Banach]]
*[[Riesz representation theorem|Riesz representation]]
*[[Closed graph theorem (functional analysis)|Closed graph]]
*[[Uniform boundedness principle]]
*[[Kakutani fixed-point theorem#Infinite-dimensional generalizations|Kakutani fixed-point]]
*[[Krein–Milman theorem|Krein–Milman]]
*[[min-max theorem|Min–max]]
*[[Gelfand–Naimark theorem|Gelfand–Naimark]]
*[[Banach–Alaoglu theorem|Banach–Alaoglu]]

| group3     = Operators
| list3      = 
*[[adjoint operator|Adjoint]]
*[[bounded operator|Bounded]]
*[[compact operator|Compact]]
*[[Hilbert–Schmidt operator|Hilbert–Schmidt]]
*[[Normal operator|Normal]]
*[[Nuclear operator|Nuclear]]
*[[Trace class]]
*[[Transpose of a linear map|Transpose]]
*[[unbounded operator|Unbounded]]
*[[unitary operator|Unitary]]

| group4     = Algebras
| list4      = 
*[[Banach algebra]] 
*[[C*-algebra]] 
*[[Spectrum of a C*-algebra]] 
*[[Operator algebra]] 
*[[Group algebra of a locally compact group]] 
*[[Von Neumann algebra]]

| group5     = Open problems
| list5      = 
*[[Invariant subspace problem]] 
*[[Mahler's conjecture]]

| group6     = Applications
| list6      = 
*[[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 (mathematics)|Distribution]] (or [[Generalized function]]s)

| group7     = Advanced topics 
| list7      = 
*[[Approximation property]] 
*[[Balanced set]]
*[[Choquet theory]]
*[[Weak topology]] 
*[[Banach–Mazur distance]] 
*[[Tomita–Takesaki theory]]

| below =
* ((icon|category)) [[:Category:Functional analysis|Category]]

))
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