Template:Functional analysis

v t e Functional analysis (topics)
Topological vector spaces	Asplund Banach (list) Banach lattice Barrelled Bornological Brauner F-space Fréchet (tame) Hilbert (Inner product space Polarization identity) Interpolation space LF-space Locally convex (Seminorms/Minkowski functionals) Mackey Montel Nuclear Normed (norm) Quasinormed Reflexive Riesz Semi-inner-product Smith Stereotype Strictly convex Webbed Topological tensor product (of Hilbert spaces)
Topologies of function spaces	Dual Dual space (Dual norm) Operator Ultraweak Weak (polar operator) Mackey Strong (polar operator) Ultrastrong Uniform convergence
Linear operators	Adjoint Bilinear (form operator sesquilinear) (Un)Bounded Closed Compact (on Hilbert spaces) (Dis)Continuous Densely defined Fredholm Hilbert–Schmidt Functionals (positive) Normal Nuclear Self-adjoint Strictly singular Trace class Transpose Unitary
Operator theory	Banach algebras C-algebras Spectrum (C-algebra radius) Spectral theory (of ODEs Spectral theorem) Polar decomposition Singular value decomposition
Theorems	Banach–Alaoglu Banach–Mazur Banach–Saks Banach–Schauder (open mapping) Banach–Steinhaus (Uniform boundedness) Bessel's inequality Cauchy–Schwarz inequality Closed graph Closed range Eberlein–Šmulian Freudenthal spectral Gelfand–Mazur Gelfand–Naimark Goldstine Hahn–Banach (hyperplane separation) Kakutani fixed-point Krein–Milman Lomonosov's invariant subspace Mackey–Arens Mazur's lemma M. Riesz extension Riesz representation Parseval's identity Schauder fixed-point
Analysis	Abstract Wiener space Bochner space Differentiation in Fréchet spaces Derivatives (Fréchet Gateaux functional holomorphic) Integrals (Bochner Dunford Gelfand–Pettis regulated Paley–Wiener weak) Functional calculus (Borel continuous holomorphic) Inverse function theorem (Nash–Moser theorem) Measures (Lebesgue Projection-valued Vector) Weakly measurable function
Types of sets	Absolutely convex Absorbing Affine Balanced Bounded Convex Convex cone (subset) Linear cone (subset) Radial Star-shaped Symmetric Zonotope
Subsets / set operations	Affine hull Algebraic interior (core) Bounding points Convex hull Extreme point Interior Linear span Minkowski addition Polar
Special Spaces	Absolute continuity AC $ba(\Sigma )$ c space Besov $B_{p,q}^{s}(\mathbf {R} )$ Bounded variation BV Bs space Continuous C(K) with K compact Hausdorff Hardy H^p Hilbert H Morrey–Campanato $L^{\lambda ,p}(\Omega )$ ℓ^p (ℓ^{${\infty }$}) L^p ( $L^{\infty }$ weighted) Schwartz $S\left(\mathbf {R} ^{n}\right)$ Segal–Bargmann F Sobolev W^k,p (Sobolev inequality) Test Functions D(U) and Distributions D'(U) Triebel–Lizorkin Wiener amalgam $W(X,L^{p})$
Applications	Differential operator Finite element method Mathematical formulation of quantum mechanics Ordinary Differential Equations (ODEs) Validated numerics