List of functional analysis topics
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This is a list of functional analysis topics, by Wikipedia page.
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Hilbert space
- Euclidean space
- Inner product space
- Hilbert space
- Parallelogram law
- Orthonormal basis
- Orthogonalization
- Orthogonal complement
- Gram-Schmidt process
- Legendre polynomials
- Matrices
- Normal vector
- Parseval's identity
- Riesz representation theorem
- Bra-ket notation
- Spectral theorem
- Positive-definite
- Rayleigh quotient
- Mercer's theorem
- Reproducing kernel Hilbert space
- Trace class
- Min-max theorem
- Rigged Hilbert space
- Hellinger-Toeplitz theorem
- Direct integral
- Semi-Hilbert space
Functional analysis, classic results
- Normed vector space
- Banach space
- Hahn-Banach theorem
- Dual space
- Predual
- Weak topology
- Reflexive space
- Polynomially reflexive space
- Baire category theorem
- Open mapping theorem
- Closed graph theorem
- Uniform boundedness principle
- Arzelą-Ascoli theorem
- Banach-Alaoglu theorem
- Measure of non-compactness
Operator theory
- Bounded linear operator
- Spectral theory
- Topologies on the set of operators on a Hilbert space
- 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
- Hilbert-Polya conjecture
Banach space examples
Real and complex algebras
- Uniform norm
- Matrix norm
- Spectral radius
- Normed division algebra
- Stone-Weierstrass theorem
- Banach algebra
- Star algebra
- B-star-algebra
- C-star-algebra
- Positive element
- Positive linear functional
- operator algebra
- Gelfand representation
- Gelfand-Naimark theorem
- Gelfand-Naimark-Segal construction
- Von Neumann algebra
- von Neumann double commutant theorem
- Topological ring
- Noncommutative geometry
- Disk algebra
- Colombeau algebra
Topological vector spaces
- Locally convex topological vector space
- F-space
- Barrelled space
- Frechet space
- Seminorm
- Dual pair
- Polar topology
- Polar set
- Mackey-Arens theorem
- Mackey topology
- Bourbaki-Alaoglu theorem
- Bornological space
- Montel space
Amenability
Wavelets
- Basis function
- Daubechies wavelet
- Haar wavelet
- Morlet wavelet
- Mexican hat wavelet
- Complex mexican hat wavelet
- Hermitian wavelet
- Hermitian hat 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
- Heisenberg picture
- Density matrix
- Quantum logic
- Quantum operation
- Wightman axioms
Probability
Non-linear
History
- Stefan Banach (1892-1945)
- Hugo Steinhaus (1887-1972)
- John von Neumann
- Alain Connes (born 1947)