Due to c# specification, overloaded operator can only be implemented as a public static function only. This is unlike C++ where it allows both instance and static operator function. Eric Gunnerson did comment once that is because of the simplicity.
Because of this limitation, you cannot declare an interface or an abstract class where you can define those operators and try to perform that operation on interface or an abstract class. This especially will impact generic class.
More example to come later. Sorry for bad explanation.
Update: Found a link I've seen before. http://www.lambda-computing.com/publications/articles/generics/