operatoranalyse
Operatoranalyse, or operator theory, is a branch of functional analysis that studies linear operators on function spaces, typically Banach or Hilbert spaces. It investigates how operators behave under algebraic operations, how their spectra influence dynamics, and how they can be extended or approximated. The central objects are linear operators, including bounded operators and unbounded densely defined closed operators, along with their adjoints and domains.
Key topics include the spectral theory: spectrum, point spectrum, continuous spectrum, and resolvent; and the spectral
Another major pillar is operator algebras, notably C*-algebras and von Neumann algebras, which abstract and unify
Methods include perturbation theory, dilation theory, numerical ranges, and various forms of functional calculus. Applications span
History: operator analysis grew from spectral theory of differential operators in the 19th and early 20th centuries,