What does Prospero feel entitled to in The Tempest?

Prospero in The Tempest seems to feel that he is entitled to a lot of things. The actions that he takes to stir up the tempest and begin the action of the play are all for the purpose of taking back what he feels he deserves.
The most obvious thing that Prospero feels entitled to is the title of Duke of Milan. Years ago, Prospero was the duke. However, as he tells Miranda in act 1, scene 2:

My brother and thy uncle, called Antonio—I pray thee, mark me—that a brother shouldBe so perfidious!—he whom next thyselfOf all the world I loved, and to him putThe manage of my state, as at that timeThrough all the signories it was the first,And Prospero the prime duke, being so reputedIn dignity, and for the liberal artsWithout a parallel. Those being all my study,The government I cast upon my brotherAnd to my state grew stranger, being transportedAnd rapt in secret studies (1.2.84-95).

Prospero was the Duke of Milan by legal right, and he claims that he was renowned in Milan for his dignity and education. Prospero was interested in studying and became so wrapped up in studying that he asked his brother to manage the duchy. However, as Prospero became more and more of a "stranger" to his state, his brother took over more and more of the government until he was able to stage a coup and exile Prospero. Prospero is the legal Duke of Milan; however, he himself admits to actions that sound like he neglected the management of his state. Whether he was a good ruler or not, the state should still rightfully belong to him, and therefore he feels entitled to getting this back.

Prospero also seems to feel that he is entitled to the love, loyalty, and servitude of the inhabitants of the island. In his initial scene with Ariel, when Ariel requests his liberty, Prospero reminds him that when he first found him, Ariel was trapped in a tree trunk and had been placed there by a witch. Prospero tells him,


Thy groansDid make wolves howl, and penetrate the breastsOf ever-angry bears. It was a tormentTo lay upon the damned, which SycoraxCould not again undo. It was mine art,When I arrived and heard thee, that made gapeThe pine and let thee out (1.2.340-347).

Since Prospero freed him, he feels that he is entitled to full servitude for anything that he requires of Ariel. Prospero also extends this attitude to the monster Caliban, from whom he expects service and obedience.
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