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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

Mathematics Encyclopedia

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