List Of Functional Analysis Topics
This is a
list of
functional analysis
topics
, by Wikipedia page.
Hilbert space
Euclidean space
Inner product space
Hilbert space
Parallelogram law
Orthonormal basis
Orthogonalization
Orthogonal complement
Gram-Schmidt process
Legendre polynomials
Matrices
Orthogonal matrix
Unitary matrix
Normal matrix
,
normal operator
Symmetric matrix
Hermitian operator
self-adjoint operator
,
Hermitian adjoint
Eigenvector
,
eigenvalue
,
eigenfunction
Diagonal matrix
Shift operator
Hilbert matrix
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
Unit ball
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
Arzel-Ascoli theorem
Banach-Alaoglu theorem
Measure of non-compactness
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
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-Polya 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
Star algebra
B-star-algebra
C-star-algebra
Universal C-star-algebra
Spectrum of a C-star-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
Locally convex topological vector space
Frechet space
F-space
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
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
Pure state
Fock state
,
Fock space
Density state
Coherent state
Heisenberg picture
Density matrix
Quantum logic
Quantum operation
Wightman axioms
Probability
Free probability
Non-linear
Fixed point theorems in infinite-dimensional spaces
History
Stefan Banach
(
1892
-
1945
)
Hugo Steinhaus
(
1887
-
1972
)
John von Neumann
Alain Connes
(born
1947
)
Functional analysis
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