Barnes & Noble said today that John Malone’s Liberty Media, whose holdings include entertainment businesses as diverse as QVC, Starz Media and Sirius XM Radio, has offered to buy the nation’s biggest bookstore chain for $1.02 billion. The $17-per-share offer is a 20% premium over Barnes & Noble’s closing stock price Thursday. The bookseller put itself up for sale in August amid slumping sales that already chased main rival Borders into Chapter 11 bankruptcy in February. Liberty’s proposal is “contingent on the participation of founding chairman Leonard Riggio, both in terms of his continuing equity ownership and his continuing role in management,” according to Barnes & Noble. Riggio and his brother Stephen, who’s vice chairman, together control about 31.5% of B&N stock.