List of functional analysis topics

This is a list of functional analysis topics, by Wikipedia page.

Table of contents

1 Hilbert space 2 Functional analysis, classic results 3 Real and complex algebrass 4 Topological vector spaces 5 Wavelets 6 Quantum theory 7 History

Hilbert space

• Euclidean space
• Inner product space
• Hilbert space
• Orthonormal basis
• Orthogonalization
• Gram-Schmidt process
• Legendre polynomials
• Matrices
  • Orthogonal matrix
  • Unitary matrix
  • Normal matrix, normal operator
  • Symmetric matrix
  • Hermitian operator self-adjoint operator
  • Eigenvector, eigenvalue
  • Diagonal matrix
• Normal vector
• Riesz representation theorem
• Bra-ket notation
• Spectral theorem
• Positive-definite
• Rayleigh quotient
• Mercer's theorem
• Trace class

Functional analysis, classic results

• Normed vector space
• Bounded linear operator
• Banach space
  • Lp space
  • Hardy space
• Hahn-Banach theorem
• Dual space
• Weak topology
• Reflexive space
• Baire category theorem
• Open mapping theorem
• Closed graph theorem
• Uniform boundedness principle
• Fredholm operator

Real and complex algebrass

• Stone-Weierstrass theorem
• Banach algebra
• B-star-algebra
• C-star algebra
• Gelfand representation
• Gelfand-Naimark-Segal
• Von Neumann algebra
• Topological ring
• Noncommutative geometry
• Colombeau algebra

Topological vector spaces

• Frechet space
• F-space

Wavelets

• Basis function
• Haar wavelet
• Morlet wavelet

Quantum theory

• Mathematical formulation of quantum mechanics
• Quantum state
  • Fock state, Fock space
  • Coherent state
• Heisenberg picture
• Density matrix
• Wightman axioms

History

• Stefan Banach (1892-1945)
• Hugo Steinhaus (1887-1972)
• Alain Connes (born 1947)