Why is Shakespeare's play titled Julius Caesar, even though he is dead by Act III and plays a relatively small role?

The plot of Shakespeare's play, Julius Caesar, revolves around Caesar's planned assassination, the execution of that assassination, and the inability of certain characters to reconcile their guilt over involvement in the assassination. Julius Caesar isn't what would normally be considered a "central character" in the story, and Caesar may have far fewer lines than, say, Brutus, but there would be no play without him.

Caesar plays a vital role in the plot and remains a viable character in the play even after he is dead. Brutus wants to "come by Caesar's spirit / And not dismember Caesar." Even though Brutus and the conspirators succeed in dismembering Caesar's body, what they can't do is destroy his spirit. Antony invokes the spirit of Caesar first in his soliloquy in Act III, Scene 1, and he uses it to bring the citizens of Rome to rebellion in Act III, Scene 2.

The ghost of Caesar also appears to Brutus at Sardis and again at Philippi, which shows the audience that Brutus can't bring himself to believe that he did the right thing by participating in the murder, and it also signifies that Brutus's (and Cassius's) fortunes are fading. The ghost of Julius Caesar quits being a central force in the play only after Cassius and Brutus kill themselves, each acknowledging that he is doing so to escape the spirit of Caesar.