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Concept
Operator theory
Summary
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis.
If a collection of operators forms an algebra over a field, then it is an operator algebra. The description of operator algebras is part of operator theory.
Single operator theory
Single operator theory deals with the properties and classification of operators, considered one at a time. For example, the classification of normal operators in terms of their spectra falls into this category.
Spectrum of operators
Spectral theorem
The spectral theorem is any of a number of results about linear operators or about matrices.Sunder, V.S. Functio
Official source
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