List of functional analysis topics This is a list of functional analysis topics. See also: Glossary of functional analysis. Hilbert space Bra–ket notation Definite bilinear form Direct integral Euclidean space Fundamental theorem of Hilbert spaces Gram–Schmidt process Hellinger–Toeplitz theorem Hilbert space Inner product space Legendre polynomials Matrices Mercer's theorem Min-max theorem Normal vector Orthonormal basis Orthogonal complement Orthogonalization Parallelogram law Normal matrix, normal operator Orthogonal matrix Unitary matrix Semi-Hilbert space Diagonal matrix Eigenvector, eigenvalue, eigenfunction Hermitian operator self-adjoint operator, Hermitian adjoint Hilbert matrix Shift operator Symmetric matrix Parseval's identity Rayleigh quotient Reproducing kernel Hilbert space Riesz representation theorem Rigged Hilbert space Spectral theorem, Spectral theory Trace class Functional analysis, classic results Normed vector space Unit ball Banach space Hahn–Banach theorem Dual space Predual Weak topology Reflexive space Polynomially reflexive space Baire category theorem Open mapping theorem (functional analysis) Closed graph theorem Uniform boundedness principle Arzelà–Ascoli theorem Banach–Alaoglu theorem Measure of non-compactness Banach–Mazur theorem Operator theory Bounded linear operator Continuous linear extension Compact operator Approximation property Invariant subspace Spectral theory Spectrum of an operator Essential spectrum Spectral density Topologies on the set of operators on a Hilbert space norm topology ultrastrong topology strong operator topology weak operator topology weak-star operator topology ultraweak topology Singular value (or S-number) Fredholm operator Fuglede's theorem Compression (functional analysis) Friedrichs extension Stone's theorem on one-parameter unitary groups Stone–von Neumann theorem Functional calculus Continuous functional calculus Borel functional calculus Hilbert–Pólya conjecture Banach space examples Lp space Hardy space Sobolev space Tsirelson space ba space Real and complex algebras Uniform norm Matrix norm Spectral radius Normed division algebra Stone–Weierstrass theorem Banach algebra *-algebra B*-algebra C*-algebra Universal C*-algebra Spectrum of a C*-algebra Positive element Positive linear functional operator algebra nest algebra reflexive operator algebra Calkin algebra Gelfand representation Gelfand–Naimark theorem Gelfand–Naimark–Segal construction Von Neumann algebra Abelian von Neumann algebra von Neumann double commutant theorem Commutant, bicommutant Topological ring Noncommutative geometry Disk algebra Colombeau algebra Topological vector spaces Barrelled space Bornological space Bourbaki–Alaoglu theorem Dual pair F-space Fréchet space Krein–Milman theorem Locally convex topological vector space Mackey topology Mackey–Arens theorem Montel space Polar set Polar topology Seminorm Amenability Amenable group Von Neumann conjecture Wavelets Basis function Daubechies wavelet Haar wavelet Morlet wavelet Mexican hat wavelet Complex Mexican hat wavelet Hermitian wavelet Discrete wavelet transform Continuous wavelet Continuous wavelet transform Quantum theory See also list of mathematical topics in quantum theory Mathematical formulation of quantum mechanics Observable Operator (physics) Quantum state Pure state Fock state, Fock space Density state Coherent state Heisenberg picture Density matrix Quantum logic Quantum operation Wightman axioms Probability Free probability Bernstein's theorem Non-linear Fixed-point theorems in infinite-dimensional spaces History Stefan Banach (1892–1945) Hugo Steinhaus (1887–1972) John von Neumann (1903-1957) Alain Connes (born 1947) Earliest Known Uses of Some of the Words of Mathematics: Calculus & Analysis Earliest Known Uses of Some of the Words of Mathematics: Matrices and Linear Algebra

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