List of functional analysis topics
This is a list of functional analysis topics, by Wikipedia page.
Hilbert space
- Definite bilinear form
- 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, Spectral theory
- 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
- 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
- Spectral theory
- Topologies on the set of operators on a Hilbert space
- 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
- Hilbert–Pólya conjecture
Banach space examples
Real and complex algebras
- Uniform norm
- Matrix norm
- Spectral radius
- Normed division algebra
- Stone–Weierstrass theorem
- Banach algebra
- *-algebra
- B*-algebra
- C*-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
Amenability
Wavelets
Quantum theory
Probability
Non-linear
History
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