Billionaire investor Carl Icahn turned up the heat today in his proxy fight with San Diego-based Amylin Pharmaceuticals by calling for the resignation of chairman Joseph Cook. In a letter to Amylin that was filed with the SEC, Icahn criticized Cook for destroying shareholder value. He says the company, under Cook’s stewardship, has made many grievous mistakes. “Like an ‘imperial’ chairman you have taken steps to entrench yourself that we believe to be unconscionable,” Icahn wrote. Icahn, who owns almost 10 percent of Amylin’s stock, and Eastbourne Capital Management, which owns a 12.5 percent stake, are battling to take control of the company by submitting their own candidates for the company’s board.