The Duke in "My Last Duchess" is pretty much the green-eyed monster incarnate. He’s almost an allegorical figure for jealousy. He’s jealous of the attention his wife shows to other people – even if all she does is thank them for bringing her some cherries. He’s jealous of every smile and every blush that she bestows, intentionally or unintentionally, on someone else. He’s so jealous that he can’t even bring himself to talk to her about her behavior – murder is the only solution he can come up with. His jealousy isn’t just about romantic attention; it’s about any kind of attention.
The Duke is jealous of the way the Duchess treats other people, not because he loves her and wants all her love for himself, but because he wants her to acknowledge his power over her.