An operator can only be registered if it has been implemented manually by you. Then you would register just like any other function/method.
Here are some examples from scriptstring.cpp (available in the add_on folder)
r = engine->RegisterObjectBehaviour("string", asBEHAVE_ADD_ASSIGN, "string &f(const string ∈)", asMETHODPR(asCScriptString, operator+=, (const asCScriptString&), asCScriptString&), asCALL_THISCALL); assert( r >= 0 );r = engine->RegisterGlobalBehaviour(asBEHAVE_EQUAL, "bool f(const string ∈, const string ∈)", asFUNCTIONPR(operator==, (const string &, const string &), bool), asCALL_CDECL); assert( r >= 0 );
AngelScript currently doesn't accept dual operators registered as object behaviours, except for the assignment operators. All other dual operators must be registered as global behaviours, which means that they must be implemented as global functions (or at least static member functions).