Difference between revisions of "Template:Functional analysis"

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{{Navbox
 
{{Navbox
 
| name = Functional analysis
 
| name = Functional analysis
| state = {{{state|{{{1|}}}}}}
+
| title = [[Functional analysis]] ([[List of functional analysis topics|topics]] – [[Glossary of functional analysis|glossary]])
| title = [[Functional analysis]] ([[List of functional analysis topics|topics]])
+
| listclass = hlist
| listclass = hlist
+
| state      = {{{state|}}}
  
| group1 = [[Topological vector space|TVS]] types
+
| group1     = Spaces
| list1 =
+
| list1      =
* [[Banach space|Banach]]
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  {{Navbox|subgroup
* [[Banach lattice|Banach Lattice]]
+
  | group1 =
* [[Barrelled space|Barrelled]]
+
  | list1 =
* [[Bornological space|Bornological]]
+
*[[Banach space|Banach]]  
* [[Brauner space|Brauner]]
+
*[[Besov space|Besov]]  
* [[F-space]]
+
*[[Fréchet space|Fréchet]]  
* [[Euclidean space|Finite-dimensional]]
+
*[[Hilbert space|Hilbert]]
* [[Fréchet space|Fréchet]] ([[Differentiation in Fréchet spaces#Tame Fréchet spaces|tame]])
+
*[[Hölder space|Hölder]]
* [[Hilbert space|Hilbert]] ([[Inner product space|pre-Hilbert]]
+
*[[Nuclear space|Nuclear]]
*  [[Polarization identity]])
+
*[[Orlicz space|Orlicz]]
* [[LF-space]]
+
*[[Schwartz space|Schwartz]]
* [[Locally convex topological vector space|Locally convex]] ([[Locally convex topological vector space#Definition via seminorms|Seminorm]]s/[[Minkowski functional]]s)
+
*[[Sobolev space|Sobolev]]
* [[Mackey space|Mackey]]
+
*[[topological vector space|topological vector]]
* [[Montel space|Montel]]
+
  | group2 = Properties
* [[Nuclear space|Nuclear]]
+
  | list2  =
* [[Normed space|Normed]] ([[Norm (mathematics)|norm]])
+
*[[barrelled space|barrelled]]
* [[Quasinorm|Quasinormed]]
+
*[[complete metric space|complete]]
* [[Reflexive space|Reflexive]]
+
*[[Dual space|dual]] ([[Dual space#Algebraic dual space|algebraic]]/[[Dual space#Continuous dual space|topological]])
* [[Riesz space|Riesz]]
+
*[[Locally convex topological vector space|locally convex]]  
* [[Smith space|Smith]]
+
*[[Reflexive space|reflexive]]
* [[Stereotype space|Stereotype]]
+
*[[separable space|separable]]
* [[Strictly convex space|Strictly convex]]
+
}}
* [[Webbed space|Webbed]]
 
* [[Topological tensor product]] ([[Tensor product of Hilbert spaces|of Hilbert spaces]])
 
  
| group2 = Mapping topologies
+
| group2     = Theorems
| list2 =
+
| list2     =  
* [[Dual topology|Dual]]
+
*[[Hahn–Banach theorem|Hahn–Banach]]
* [[Dual space]]&nbsp([[Dual norm]])
+
*[[Closed graph theorem (functional analysis)|closed graph]]
* [[Operator topologies|Operator]]
+
*[[uniform boundedness principle]]
* [[Ultraweak topology|Ultraweak]]
+
*[[Kakutani fixed-point theorem#Infinite-dimensional generalizations|Kakutani fixed-point]]
* [[Weak topology|Weak]] ([[Weak operator topology|operator]])
+
*[[Krein–Milman theorem|Krein–Milman]]
* [[Mackey topology|Mackey ]]
+
*[[min-max theorem|min–max]]
* [[Strong topology|Strong]] ([[Strong topology (polar topology)|polar]]
+
*[[Gelfand–Naimark theorem|Gelfand–Naimark]]
*   [[Strong operator topology|operator]])
+
*[[Banach–Alaoglu theorem|Banach–Alaoglu]]
* [[Ultrastrong topology|Ultrastrong]]
 
* [[Topology of uniform convergence|Uniform convergence]]
 
  
| group3 = [[Linear map|Linear operators]]
+
| group3     = Operators
| list3 =
+
| list3     =  
* [[Hermitian adjoint|Adjoint]]
+
*[[adjoint operator|adjoint]]
* [[Bilinear map|Bilinear]] ([[Bilinear form|form]]
+
*[[bounded operator|bounded]]
*  [[Bilinear map|operator]]
+
*[[compact operator|compact]]
*  [[Sesquilinear form|sesquilinear]])
+
*[[Hilbert–Schmidt operator|Hilbert–Schmidt]]
* ([[Unbounded operator|Un]])[[Bounded operator|Bounded]]
+
*[[Normal operator|normal]]
* [[Closed linear operator|Closed]]
+
*[[Nuclear operator|nuclear]]
* [[Compact operator|Compact]]
+
*[[trace class]]
* ([[Discontinuous linear map|Dis]])[[Continuous linear operator|Continuous]]
+
*[[unbounded operator|unbounded]]
* [[Densely defined]]
+
*[[unitary operator|unitary]]
* [[Fredholm operator|Fredholm]]
 
* [[Hilbert–Schmidt operator|Hilbert–Schmidt]]
 
* [[Linear form|Functionals]] ([[Positive linear functional|positive]])
 
* [[Normal operator|Normal]]
 
* [[Nuclear operator|Nuclear]]
 
* [[Self-adjoint operator|Self-adjoint]]
 
* [[Strictly singular operator|Strictly singular]]
 
* [[Trace class]]
 
* [[Transpose of a linear map|Transpose]]
 
* [[Unitary operator|Unitary]]
 
  
| group4 = [[Operator theory]]
+
| group4     = Algebras
| list4 =
+
| list4     =  
* [[Banach algebra]]s
+
*[[Banach algebra]]  
* [[C*-algebra]]s
+
*[[C*-algebra]]  
* [[Spectrum (functional analysis)|Spectrum]] ([[Spectrum of a C*-algebra|C*-algebra]]
+
*[[spectrum of a C*-algebra]]  
*   [[Spectral radius|radius]])
+
*[[operator algebra]]  
* [[Spectral theory]] ([[Spectral theory of ordinary differential equations|of ODEs]]
+
*[[group algebra of a locally compact group]]  
*   [[Spectral theorem]])
+
*[[von Neumann algebra]]
* [[Polar decomposition]]
 
* [[Singular value decomposition]]
 
  
|group5 = Theorems
+
| group5     = Open problems
|list5 =
+
| list5     =  
* [[Banach–Alaoglu theorem|Banach–Alaoglu]]
+
*[[invariant subspace problem]]  
* [[Banach–Mazur theorem|Banach–Mazur]]
+
*[[Mahler's conjecture]]
* [[Banach–Saks theorem|Banach–Saks]]
 
* [[Bessel's inequality]]
 
* [[Cauchy–Schwarz inequality]]
 
* [[Closed graph theorem|Closed graph]]
 
* [[Closed range theorem|Closed range]]
 
* [[Eberlein–Šmulian theorem|Eberlein–Šmulian]]
 
* [[Freudenthal spectral theorem|Freudenthal spectral]]
 
* [[Gelfand–Mazur theorem|Gelfand–Mazur]]
 
* [[Gelfand–Naimark theorem|Gelfand–Naimark]]
 
* [[Goldstine theorem|Goldstine]]
 
* [[Hahn–Banach theorem|Hahn–Banach]] ([[Hyperplane separation theorem|hyperplane separation]])
 
* [[Kakutani fixed-point theorem#Infinite-dimensional generalizations|Kakutani fixed-point]]
 
* [[Krein–Milman theorem|Krein–Milman]]
 
* [[Invariant subspace problem#Known special cases|Lomonosov's invariant subspace]]
 
* [[Mackey–Arens theorem|Mackey–Arens]]
 
* [[Mazur's lemma]]
 
* [[M. Riesz extension theorem|M. Riesz extension]]
 
* [[Riesz representation theorem|Riesz representation]]
 
* [[Open mapping theorem (functional analysis)|Open mapping]]
 
* [[Parseval's identity]]
 
* [[Schauder fixed-point theorem|Schauder fixed-point]]
 
  
| group6 = Analysis
+
| group6     = Applications
| list6 =
+
| list6     =  
* [[Abstract Wiener space]]
+
*[[Hardy space]]  
* [[Bochner space]]
+
*[[spectral theory of ordinary differential equations]]  
* [[Differentiation in Fréchet spaces]]
+
*[[heat kernel]]  
* [[Derivative]]s ([[Fréchet derivative|Fréchet]]
+
*[[index theorem]]  
*  [[Gâteaux derivative|Gâteaux]]
+
*[[calculus of variation]]  
*  [[Functional derivative|functional]]
+
*[[functional calculus]]  
*  [[Infinite-dimensional holomorphy|holomorphic]])
+
*[[integral operator]]  
* [[Integral]]s ([[Bochner integral|Bochner]]
+
*[[Jones polynomial]]  
*  [[Dunford integral|Dunford]]
+
*[[topological quantum field theory]]  
*  [[Pettis integral|Gelfand–Pettis]]
+
*[[noncommutative geometry]]  
*  [[Regulated integral|regulated]]
+
*[[Riemann hypothesis]]
*  [[Paley–Wiener integral|Paley–Wiener]]
 
*  [[Pettis integral|weak]])
 
* [[Functional calculus]] ([[Borel functional calculus|Borel]]
 
*   [[Continuous functional calculus|continuous]]
 
*   [[Holomorphic functional calculus|holomorphic]])
 
* [[Inverse function theorem]] ([[Nash–Moser theorem]])
 
* Measures ([[Infinite-dimensional Lebesgue measure|Lebesgue]]
 
*   [[Projection-valued measure|Projection-valued]]
 
*  [[Euclidean vector|Vector]])
 
* [[Weakly measurable function]]
 
  
| group7 = Types of sets
+
| group7     = Advanced topics
| list7 =
+
| list7     =  
* [[Absolutely convex set|Absolutely convex]]
+
*[[approximation property]]  
* [[Absorbing set|Absorbing]]
+
*[[balanced set]]  
* [[Balanced set|Balanced]]
+
*[[weak topology]]  
* [[Bounded set (topological vector space)|Bounded]]
+
*[[Banach–Mazur distance]]  
* [[Convex set|Convex]]
+
*[[Tomita–Takesaki theory]]
* [[Convex cone|Convex cone {{smaller|(subset)}}]]
 
* [[Cone (linear algebra)|Linear cone {{smaller|(subset)}}]]
 
* [[Radial set|Radial]]
 
* [[Star domain|Star-shaped]]
 
* [[Symmetric set|Symmetric]]
 
* [[Zonotope]]
 
  
| group8 = Subsets{{\}}set operations
+
<!-- ... -->
| list8 =
 
* [[Algebraic interior|Algebraic interior (core)]]
 
* [[Bounding point]]s
 
* [[Convex hull]]
 
* [[Extreme point]]
 
* [[Interior (topology)|Interior]]
 
* [[Minkowski addition|Minkowski addition]]
 
* [[Polar set|Polar]]
 
 
 
}}<noinclude>
 
{{Documentation
 
| content =
 
{{Collapsible option |statename=optional}}
 
 
}}
 
}}
 
+
<noinclude>
 
[[Category:Mathematics navigational boxes]]
 
[[Category:Mathematics navigational boxes]]
 +
[[Category:Functional analysis|*]]
 
</noinclude>
 
</noinclude>

Latest revision as of 08:02, 11 January 2021