Depending on this question I am totally confused now, when to define something as an operator or as an ordinary math symbol. egreg says in his comment that the identity function is to be used as an ordinary math symbol rather than as a operator. I would like to understand the reason for this.
Is there any thumb rule, when to declare something as an operator and when to define something a an ordinary math symbol?
For instance, I have seen in source files that one defines the adjoint action, as the following:
but egreg suggests to define the identity function like this
What is the underlying principle which leads to this kind of usage?