Junior’s Restaurant has earned a lot of superlatives since it opened in Downtown Brooklyn on Election Day in 1950, among them the one that adorns every orange takeout box: “The Best Cheesecake in N.Y. — New York Magazine” (a distinction that dates to 1973, but still).

It was headed for another distinction this year, when Alan Rosen, who took over the business in 1992 and whose family has owned the restaurant since its first cheesecake, decided to sell the two-story building. In a neighborhood where real estate brokers talk about record-setting prices and rents the way pilots used to talk about breaking the sound barrier, the sale was major news. Offers to buy and build an apartment tower poured in from Brooklyn, Manhattan and abroad. The highest bid: $450 per buildable square foot, well over the previous high for Brooklyn of $350, for a total of $45 million in cash.

“That’s a lot of cheesecake,” said Mr. Rosen — who, nevertheless, and after much agonizing, a visit to his therapist and a series of sleepless nights, turned it down.

“This is Junior’s identity, is this building. This is the one where I came on my first dates. It’s where my family spent most of their waking hours,” he said in an interview on Monday, about a week after making his decision, as he contemplated his stewardship of a legend in Brooklyn. “Not the one down the street, not the one below 20 stories of condos. This one.”