Describe the relationship between Willy and his sons as Ben influences them as a family in Death of a Salesman.

Ben Loman represents a
story and standard of success that Willy adopts for himself and his sons. In this way, Ben
becomes a symbol of success that reflects Willy's failure. He also becomes an ideological tool -
an intellectual concept - which serves to distance Willy, Biff and Happy from reality and also
to distance them from one another. 

Primarily, we can see Ben as a symbol
(and a symptom) of Willy's persistent and complex delusions regarding success. 

He appears in scenes which take place in Willy's imagination, and
appears larger-than-life, all-knowing, powerful, a great adventurer; he is everything Willy
dreams of becoming.

As a young man, Ben sets off to seek
his fortune. After living in the wilds of Alaska and Africa, Ben succeeds in his adventures and
becomes quite wealthy.

Willy states directly that he sees Ben as a great
example for his own boys. Willy reminds Biff and Happy about the greatness of their uncle and
seems to fully expect them to achieve similar things. 

While Biff realizes
that this potential simply is not in him and ultimately faces up to the reality of his
character, Happy internalizes the dream that Willy repeated so often. This becomes perfectly
clear at Willy's funeral, when Happy offers his take on Willy's character. 

"I'm gonna show you and everybody else that Willy Loman did not
die in vain. He had a good dream. It's the only dream you can haveto come out number-one man. He
fought it out here, and this is where I'm gonna win it for him."

Willy's high expectations for himself and for his two sons proves
damaging all around. The schism that so plainly exists in Willy's mind regarding who he truly is
and who he believes himself to be leads to a moral failing in Willy, demonstrated by the affair
that Biff discovers in Boston. 

Unable to accept his station in life and
unsatisfied with his modest achievements, Willy defends himself through bluster and lies both to
Biff and to his neighbor Charlie. Willy's talent for delusion and his preference for fantasy
both lead Biff to steal as a child and to attempt to get a loan from his old boss as an
adult.

Biff comes to realize that this elevated self-regard is nothing more
than fantasy. He attempts to bring his father around to this realization as well, but Willy
feels that Biff is simply attacking him again. Willy clings to the notion that he once was
"somebody" and that his brother Ben still stands as an example of achievement suited
to his own personality, or at least that of his sons.

Biff, it appears, comes to the sad realization that his father "didn't know who he
was," and how his father's unrealistic dreams led him away from the satisfaction he could
have found if he had pursued a goal that reflected his talents...