Death of a Salesman and tragedy

Classical Tragedy
According to Aristotle's Poetics, tragedy involves a protagonist of high estate who falls from prosperity to misery through a series of reversals and discoveries as a result of a "tragic flaw," (hamartia) generally an error caused by human frailty. Aside from this initial moral weakness or error, the protagonist is basically a good person. In Aristotelian tragedy, the action generally involves revolution (unanticipated reversals of what is expected to occur) and discovery (in which the protagonists and audience learn something that had been hidden). The third part of the fable, disasters, includes all destructive actions, deaths, etc. Tragedy evokes pity and fear in the audience, leading finally to catharsis (the purgation of these passions).

Arthur Miller followed his first success (All My Sons 1947) with what has become the great American modern classic, Death of a Salesman. It stunned audiences with its brilliance and was quickly earmarked as a classic of the modern theatre. It also sparked heated debates over the true nature of tragedy. Some critics criticized Miller for infusing the play with a deep sense of pity for the commonplace salesman Willy Loman. They insisted that Willy was a "little man" and therefore not worthy of the pathos reserved for such tragic heroes as Oedipus and Medea. Miller, however, argued that the tragic feeling is invoked whenever we are in the presence of a character, any character, who is ready to sacrifice his life, if need be, to secure one thing--his sense of personal dignity. And the "little" salesman wasdetermined to do just that, no matter what the cost.

Is Willy Loman a tragic hero?

Willy Loman is not a classical tragic hero, given the definition above. Rather, he is what’s known as an “antihero.” This is a more common figure in modern tragedy, since the modern age tends to lack clear-cut ethics and morals by which to judge its heroes.
The antihero, instead of manifesting dignity, power, and heroism, tends to manifest passivity and ineffectualness. This is not altogether the case with Willy—he has, in spite of his unexalted nature, a certain innate dignity about him.
Willy does, however, have a tragic flaw—and it relates directly to hamartia as an “error of judgement”—what is Willy’s error? (that style can get you farther than either hard work or skill)
This ties into the idea of hubris in a bit of a skewed way. Ordinarily, hubris, because it results from a kind of arrogance, is a conscious attempt to outwit fate or transcend moral law. In Willy’s case, this is not really conscious—that is, he attempts to break a moral law, but one that he doesn’t really recognize as moral. The moral law he consciously breaks leads not to his own downfall so much as the downfall (or the redemption) of Biff.
One other typically modern feature of this play is that it does not, as classical tragedies do, move the hero from an exalted position to an abased one. Rather, the hero is already near the bottom of the wheel of fortune when the play begins.