Are there any other unary operators possible in Boolean logic?

For each value of p there are two choices for the value that an operator will produce. The Negation operator implements one of those choices, namely that every literal is converted to the other literal in the collection.

It is possible to define another operator that converts every literal to its own value, namely an operator that does nothing. Such an operator is interesting from the standpoint of completeness but is not usually discussed in Boolean logic

It is possible to define yet another operator that converts every literal to T, namely an operator that doesn't care what is in the left column. Additionally we can define a similar operator that converts every literal to F. Again, these operators are interesting from the standpoint of completeness but are not usually discussed in Boolean logic.