Sears is considering selling its popular Kenmore appliance brand and other divisions after the hedge fund run by CEO Edward Lampert expressed interest in buying them and breaking up the company.

Sears' board is beginning a formal process to explore the sale of three pieces of the business Lampert's ESL Investments expressed interest in acquiring: Kenmore, the home improvement business of the Sears Home Services Division, and the Parts Direct business of Sears Home Services, the retailer said Monday.

As of Monday morning, Sears' shares shot up about 6 percent over last week's closing price.

Sears Holdings Corp. has been exploring alternatives for those businesses — as well as the Craftsman tools and DieHard battery brands — for nearly two years, saying it believes they have room to grow by expanding their reach beyond Sears. But after failing to find a buyer for assets other than Craftsman, ESL told Sears in a letter last month it should “aggressively pursue divestiture” of all or some of those businesses.

ESL had also offered to buy certain Sears real estate assets, including debt, and continue to lease the properties to Sears or other entities.

Sears' board has established a committee to evaluate ESL Investments' proposal and seek other offers for Kenmore and the other divisions, the retailer said.

ESL previously said it would not purchase the businesses unless the deal was recommended by the committee and approved by a majority of disinterested shareholders. The investment firm also said Lampert and Kunal Kamlani, president of ESL and a member of Sears' board, would not participate in sale discussions.