Maggie Gyllenhaal may come from a family of filmmakers, yet she never let herself dream about directing until recently. Things changed very quickly and very profoundly for Gyllenhaal when she found herself writing to Elena Ferrante, asking for permission to adapt her 2008 novel “The Lost Daughter.”

Ferrante said yes, she could have the rights, but there was one condition: Gyllenhaal had to direct it herself or the contract was “null and void.” “I think I’ve always been a director and I just didn’t feel entitled to admit it to myself,” Gyllenhaal said Friday at the Venice Film Festival before her film makes its world premiere in competition. “I think it’s a better job for me actually.”