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