, operator theory
is the branch of functional analysis
which deals with bounded linear operators
and their properties. It can be split crudely into two branches, although there is considerable overlap and interplay between them. These extend the spectral theory
for bounded 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.
The theory of operator algebras
of operators such as C*-algebras
to the fore.