Well, it's not really an operator-- it's the 'be' verb; sorry. An operator is the part of a verb phrase that changes tense/person:
'He must certainly be mad'-- operator is 'must' and adverb most commonly goes right after it. 'I have never gone skiing' -- operator is 'have' 'We are waiting for you' -- operator is 'are'
Adverbs are highly mobile. The positioning that Mr M described so well represents the normal neutral position of adverbs. Moved to other locations, they create nuances. Some of these can be quite different, most probably just intensify a bit.