Operator theory

In mathematics, operator theory is the branch of functional analysis that focuses on bounded linear operators, but which includes closed operators and nonlinear operators.

Operator theory also includes the study of algebras of operators.

Single operator theory

Single operator theory deals with the properties and classification of single operators. For example, the classification of normal operators in terms of their spectra falls into this category.

Operator algebras

The theory of operator algebras brings algebras of operators such as C*-algebras to the fore.

See also

• Invariant subspace
• Functional calculus
• Spectral theory
  • Resolvent formalism
• Compact operator
  • Fredholm theory of integral equations
    • Integral operator
    • Fredholm operator
• Self-adjoint operator
• Unbounded operator
  • Differential operator
• Umbral calculus
• Contraction mapping
• Positive operator on a Hilbert space
• Nonnegative operator on a partially ordered vector space

External links

• History of Operator Theory