(Reuters) - A hedge fund owned by the chief executive of Sears Holdings Corp (SHLD.O), Edward Lampert, has offered to buy the company’s Kenmore appliances brand for $400 million in cash, Sears said in a regulatory filing on Tuesday. ESL Investments also made an offer to buy the Home Improvement business of the company’s home services division for as much as $80 million in cash, according to the filing with the U.S. Securities and Exchange Commission. The offer for Kenmore is conditional on ESL receiving equity financing from a potential partner, according to the filing. No partner was named.