Operators in English grammar are words that facilitate the expression of a negation, interrogatives, and emphasis.
Operator is a grammatical function.
The grammatical form that can function as the operator in English grammar is the verb phrase. The only auxiliary verb that can function as the operator are the verb do.
Operators are constituents of the verb phrase.
Brinton, Laurel J. & Donna M. Brinton. 2010. The linguistic structure of Modern English, 2nd edn. Amsterdam: John Benjamins Publishing Company.
Hopper, Paul J. 1999. A short course in grammar. New York: W. W. Norton & Company.
Huddleston, Rodney. 1984. Introduction to the grammar of English. Cambridge: Cambridge University Press.