Your syntax is a little unclear, but I think I get the gist of what you're asking.

In your first example, I'm assuming "obj" is typed as Object. If that's the case, you're casting is telling the compiler that you know it is specifically of type E. Since Object is the super-type of everything, I believe this is possible and the compiler will let you do it, but you are risking a ClassCastException at runtime if you're wrong.

It's conceptually similar in the second example, but I think it depends on whether or not the compiler can determine that E is a subtype of A. I assume this is meant to read as "E element = (E) a" where "a" is of type "A".

I'm assuming the last example is supposed to be "Object obj = (Object) e", where "e" is of type "E". This you can always do because Object is a super-type of every other type. In this case, the cast expression isn't even necessary because the compiler already knows that every value is an Object.