In physics, an operator is a function over a space of physical states to another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are a very useful tool in classical mechanics.
value categories (lvalue, rvalue, xvalue). order of evaluation (sequence points). constant expressions. unevaluated expressions. primary expressions. lambda-expression(C++11). Literals. integer literals. floating-point literals. boolean literals. character literals including escape sequences. string literals. null...
In mathematics, an operator is generally a mapping that acts on the elements of a space to produce other elements of the same space. The most common operators are linear maps, which act on vector spaces.
In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases.
In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings. Although it is usually classified as a branch of functional analysis, it has direct applications to representation theory...