Operátort

Operátort is the accusative singular form of operátor in several languages, and the term itself is used to denote a person who operates something, as well as to refer to a class of abstract or technical concepts in various fields. In general usage, an operator is someone who controls, drives, or runs a device or system. In mathematics and computer science, the word has a more specific meaning as well.

In mathematics, an operator is a mapping that takes elements from one set to another, typically between function spaces. Linear operators act on vector spaces and satisfy linearity. Examples include the identity operator, differentiation, and integral operators. Operators can be bounded or unbounded, defined on certain domains, and studied through properties such as adjoints, spectra, and closure. Operator theory investigates how these mappings behave, interact, and form algebraic structures.

In programming, an operator is a symbolic token that applies to operands to yield a result, such as arithmetic (+, −, ×, ÷), relational (>, <), or logical operators. Operators participate in expressions according to precedence rules, and some languages support operator overloading to extend their meaning for user-defined types.

In physics, operators represent observable quantities or physical processes, with the expectation values and spectra describing measurable properties. Quantum mechanics, for example, uses operators to encode measurements and evolutions.

In industry and services, an operator may refer to a person who operates machinery (machine operator), a telecommunications service provider (mobile or landline operator), or an entity that manages a system such as a power grid or transport service.

Etymology traces back to Latin operari, meaning to work. See also operator.