Is Hamlet the protagonist or the antagonist of the play or both?

Hamlet is the protagonist of the play and Claudius would be considered the antagonist of the play. The entire play deals with Hamlet's quandary over how to deal with his father's death at the hand of Claudius. Once Claudius sees Hamlet as a threat, especially after seeing the play "The Mousetrap", Claudius becomes a real enemy of Hamlet and seeks to kill Hamlet. First, Claudius tries to send Hamlet to England and have the English king kill his nephew and when that fails, he plots to poison Hamlet. That certainly qualifies him as the antagonist. It's true Hamlet does wrestle with his conscience a great deal during the play, but that does not absolve Claudius from opposing Hamlet to the degree of wanting to take his life.