The two ghosts are similar in these texts in the way that the characters who are left alive--and namely the sons--are so dominated and influenced by the lives of those who have died. We can see this clearly in Hamlet's obsession with the death of his father and the way that the Ghost's appeal to Hamlet to avenge his murder dominates him psychologically. He spends the rest of the play trying to work out how to respond to his father's plea and also trying to ascertain whether the Ghost is truthful or not.
In the same way, the presence of Eben's dead mother, although she never actually appears in the play, is almost tangible in terms of the legacy that she leaves. Eben is a character who is presented as being profoundly loyal to the memory of his mother, who he feels was exploited by his father. What is particularly interesting about the adulterous union between Eben and Abby is that their adultery is committed "with a horribly frank mixture of lust and mother love." Abby declares that she will assume the role of Eben's dead mother, and their relationship therefore assumes an incestuous significance.
Both texts show how the lives of those still living is impacted by those who are dead and buried. In a very real sense, Eben's mother and Old Hamlet live on past their death through the influence they have on the characters they have left.