Nozawa, 57, died of a brain hemorrhage after the fight Sunday night, Sylt Chief Public Prosecutor Rüdiger Meienburg said.
Two men, 50 and 36, reportedly approached Nozawa in a club Sunday night after they had eaten a meal prepared by the chef earlier in the day, German paper Sylt Rundschau reported. The three men got into a physical confrontation around 2 a.m. Monday, which resulted in Nozawa's fatal injuries.
Neither of the men has been arrested as police lack strong enough evidence to issue a warrant, Flensburg prosecutor Ulrike Stahlmann-Liebelt said.
Nozawa's sister, who lives in Berlin, told the paper they were suspicious of the police's failure to make an arrest.
"It almost felt as if they would protect someone," she said, and implored employees of the bar to come forward with their accounts of the confrontation.
"My ex-husband was not aggressive, he would never have started a fight," said You Nozawa, who came with their 15-year-old son to Sylt after Nozawa's death. "He never would have started a fight."
"We have heard that the men wanted to get back their ten euros for the food," she said. "We see this as a racist act."
You Nozawa claimed her ex, who had been operating a snack bar on Sylt since April, had faced racist taunts, including being called a "gook."
Nozawa was known for his Japanese-Italian fusion dishes and had cooked for Mikhail Gorbachev, Phil Collins and Denzel Washington.
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