Answer:
In the poem, the Duke is very overprotective of the paint, when he declares "since none puts by The curtain I have drawn for you, but I" meaning no one will touch it but him. At the same time, he is using a lot of details about her dead wife and shows his jealousy when he says "not Her husband’s presence only called that spot Of joy into the Duchess’ cheek" she was too kind with everyone, not only with him and he wanted to be the only attention of her, "She thanked men—good! but thanked Somehow—I know not how—as if she ranked My gift of a nine-hundred-years-old name". In that phrase, he claims to be an important figure.
He seems overly proud of the paint, but with more interest at the end of meeting and marrying a new woman "Though his fair daughter’s self, as I avowed At starting, is my object. Nay, we’ll go Together down, sir." The poem shows that he was not a nice man but superficial and depreciable.