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An operator is a map from function space to function space. If the range of an operator is on the real line or in the complex plane, the operator is usually called a functional instead.

An operator is also a person who makes phone connections, though this practice is becoming less common as the process becomes more automated.

More generally, an operator can refer to anyone who operates heavy or complicated machinery. Examples: forklift operator, radar operator, system operator (sysop).