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# 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

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