In "Death of a Salesman," Willy Loman promises the woman in the hotel room a better life, expressing his desperate desire to escape personal failures. These promises reflect Willy's distorted perception of success and a coping mechanism for life's challenges.
The reference to "the woman" in your question likely pertains to the character Willy Loman from Arthur Miller's play "Death of a Salesman." In the hotel room scene, Willy is depicted having an extramarital affair. He promises "the woman" the illusion of a better life. Willy, struggling with his own insecurities and disillusionment, makes promises to the woman about providing financial support and a future together. However, these promises are more reflective of Willy's desperate desire to escape his own failures and inadequacies than any genuine commitment. The affair becomes a manifestation of Willy's distorted perception of success and happiness, as he seeks solace in a fantasy world to cope with the harsh realities of his own life and the challenges he faces as a salesman.