Endomorphism - Operator Theory

Operator Theory

In any concrete category, especially for vector spaces, endomorphisms are maps from a set into itself, and may be interpreted as unary operators on that set, acting on the elements, and allowing to define the notion of orbits of elements, etc.

Depending on the additional structure defined for the category at hand (topology, metric, ...), such operators can have properties like continuity, boundedness, and so on. More details should be found in the article about operator theory.