An elevator installation has an elevator car carrier that can be displaced in a travel space, a first elevator car arranged on the carrier in an adjustable manner, and a second elevator car arranged on the carrier. A drive unit on the carrier drives a traction device to adjust the first elevator car relative to the carrier. The traction device forms a closed loop and is guided over a drive roller and at least one guide roller, which rollers are arranged on the carrier. The guide roller is displaceable on the carrier to set tensioning of the traction device.