Brake equipment, for an elevator installation, includes: a static element; a movable element movable relative to the static element in a first degree of freedom, wherein selectably a first frictional contact is produced in a first contact surface between the static element and the movable element by a controllable normal force acting in a second degree of freedom, and a first friction force opposes movement of the movable element relative to the static element; and a relative element, wherein a second frictional contact is produced in a second contact surface between the movable element and the relative element by the normal force, and a second friction force opposes movement of the movable element relative to the relative element. The relative element is movable in the first degree of freedom relative to the static element between a normal position and a braking position and is resiliently biased into the normal position.