But Perry is a very involved owner, visiting the store four or five times a week. He pushed to give Freds, a popular lunch spot, a locavore twist at night to draw a bigger crowd. This past summer he organized a two-day “odyssey” to California, so that he, Lee and Vitale could learn the latest e-commerce technology. (The company’s Web site had been neglected for years, but after a revamp this past May, traffic is up 34 percent, and Lee says that Barneys.com will soon overtake the Beverly Hills store as the second-largest revenue producer after Madison Avenue.) Lee called Perry “a worthy owner-patron of Barneys,” and said: “It would be much harder if someone said, ‘We should put sneakers on the ground floor because we could sell a lot of Keds.’ That would be a problem.”

When I asked Perry whom he trusts for information about the industry, he identified Lee, Vitale and his wife. He’s certainly loyal. Lee and Vitale, another Gucci alumna, are both well regarded, but I wondered how he could be so sure his managers were as good as he thinks they are. He said he had hired a top consultant to evaluate them. “Barneys has the highest expert score of any company he’s looked at,” Perry said in earnest. “He told me he had never seen scores like this.” But scores can’t account for instinct. Lee and Vitale missed the boat on one of the most anticipated lines of the year: Raf Simons’s debut collection for Dior. Simons, a 44-year-old Belgian, had attracted notice for his modern tailoring and colors at Jil Sander, and insiders knew he had the maturity to take over a big French house. The head of another New York store told me, “We knew this was going to be big.” Lee explained in an e-mail in late October that Barneys has tended to focus on smaller European companies, like Lanvin and Givenchy, rather than the goliaths like Dior. But when I saw the Barneys team at the Paris ready-to-wear shows in September, they were champing to get Simons’s collection. Bergdorf’s and Saks will have it instead.

Perry’s arrival poses an even more fundamental question: What are stores for today? He takes ownership at a critical time for luxury retail, when stores are trying to figure out the relationship between e-commerce and bricks-and-mortar locations, and customers seem to bounce back and forth between wanting to price-hunt designer brands online and wanting to have the singular experience that a well-run store can provide. But Perry seems interested in the challenge. “The reason I didn’t want to sell it,” he said, “is that in all aspects of where retailing is headed in the future — Barneys is there. It has the in-store experience, Freds, the new shoe floor, everyone, men and women, trying on shoes together, the furniture is cool.” He believes that Barneys can be a $1 billion business, with the Web as the key driver. “In terms of the future of where e-commerce is going,” he told me in November, “I don’t think anyone’s started yet.”

It stands to reason that in the post-recession, post-postmodern era, when a lot of consumers just want what they want — without irony, without attitude, without too many barriers — that Barneys is once again reflecting the city. More and more of the shoppers you see on Madison Avenue or in the department stores are tourists. And maybe to appeal to them, Barneys must be a little less quirky and provocative and local, and more of an accessible global brand with a glossy emporium. At least that seems to be the thinking of the current management. And there are some indications that this approach is starting to pay off: company revenues in the most recent fiscal year were over $750 million, and Lee says that earnings are in line to return shortly to historic 2007 levels (which other sources put at $77 million before interest, taxes, depreciation and amortization). The Madison Avenue store now carries 1,800 different units of leather accessories (though not all displayed at once), a number that, as Lee said, reflects today’s reality: “Every inch counts.” Annual sales of those accessories have doubled to nearly $8,000 per square foot — another sign that Lee is giving consumers what they want.

But Barneys has never been about giving customers what they want. It has been about educating, expanding horizons, presenting the unexpected. “If you give your customers what they want, then you die,” Gene said. “The fact is they don’t know what they want.” Finding out what they want is one reason people still go to stores. One doesn’t search Amazon for ideas and inspiration.

Of all the ideas I heard in the course of my reporting, only Gene’s notion of open windows tingled with 21st-century possibility. It was one of those gateway ideas that immediately set off other thoughts: If Barneys had windows that allowed you to look right into the store, what new form would the interior take? What kinds of merchandise would be offered, and how? Would the stale trappings of luxury be stripped away? Would the stage be set for a new kind of experience? Beyond products and windows, that is what a store is for.

He may not be a retail savant like Gene Pressman, but Perry is a quick study. One day in July we were talking about the Paris haute couture shows, and Simons’s debut at Dior, when he said: “I thought it was great. I talked to Mark yesterday, and I didn’t get the feeling he was blown away by it. I looked at the dresses that Raf chose, and it seemed that it was right in line with what he should have done for his first collection.” My ears perked up: So Perry was aiming high. Was that instinct? A few days later, I spoke to the chief of another New York store, who said: “Barneys should be thinking of a big French brand that can go up against Chanel. Why not? There’s an opportunity there.”

Richard Perry, hedge-fund manager, might just be a retailer yet.