The anchor piece (3) and the functional piece (4) in the hollow interior of the vessel are formed of a tubular stent which expands radially. The stent rests against the inside of the vessel wall (1) under radially outwardly directed elastic pretension. The stent tapers near the functional part towards the longitudinal middle axis, to form the functional part. The stent consists of wire mesh or fabric over its entire length which is constricted (5) at the narrowest point of the taper.