All along, Svetlana Aronov's family and friends held out hope.

They distributed fliers. They created a Web site. They announced a $25,000 reward. Eventually, Aronov's husband, Dr. Alexander Aronov, returned to work, and their oldest daughter, Polina, returned home to care for her sister, Veronica, 9.

Yesterday, when two detectives pulled up in front of the family's York Avenue building, hope disappeared.

The residents returning from walking their dogs knew. The doorman knew. And, moments later, Aronov's family knew: the 44-year-old rare-book dealer had been identified as the corpse pulled from the East River the day before.

Throughout the day, relatives and close friends streamed into the building to offer their condolences. "They're getting lots of visitors," the doorman said.

A woman who answered the phone at the family's 11th-floor apartment said no one was up to talking. "You can understand that," she said.

Many of the residents interviewed outside the family's building offered a theory of what happened.

"I believe she was killed," said one resident, Sue Koff, 54. "I don't believe her husband killed her, though. He's a very nice guy and they always looked very happy together."

Another woman, Beverly Hart, who has lived in the building for 35 years, said she believed Svetlana Aronov was the victim of foul play.

"This sounds like a murder to me," Hart said.

What about the possibility she killed herself, she was asked.

"No way, because she wouldn't have killed the dog," Hart said. "Why would she? She loved that dog. Why would she do that?"

In the aftermath of Aronov's disappearance in March, the building was abuzz with gossip, some residents said.

One man who lives down the hall from the family admitted yesterday that in an awkward moment he even suggested to Polina that if her mom had run away from home she might still be alive.

It was a warped way of thinking, he said, but it was the only comfort he could offer the daughter, who agreed with his assessment of the situation.

Another resident, Willow James, knew the dead woman only from seeing her walking her father's dog, Bim.

"I have a little dog and I would talk to her dog," James said. "I'm just in shock over this. I'm so sorry. I can't imagine the grief the family must be feeling."