List of Functional Analysis Topics - Operator Theory

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–Pólya conjecture

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