bearing is arranged on an inner face 2 of a bearing receiving member 3 which inner face is directed toward the rotation axis 1 the bearing receiving member 3 is arranged with an outer face 4 on a housing fixed in position an inner ring of the rolling bearing is spaced apart from the outer face of the shaft by a back up bearing gap as long as the shaft is supported in the magnetic bearings the bearing arrangement is part of the bearing of a shaft of a compressor rotating at rotary speeds of approximately 6000 rpm and being of solid construction if the magnetic bearing fails the shaft falls into the back up bearing the rolling bearing is substantially free in a radial direction and can therefore take up forces in particular in an axial direction but can take up forces in a radial direction only to a limited extent and transmit them to the housing the rolling bearing is therefore constructed so as to be rigid in an axial direction and so as to be resilient in a radial direction perpendicularly to the extent of the rotation axis 1 of the shaft in order to arrange the rolling bearing so as to be substantially free in a radial direction there is provision for the bearing receiving member 3 on which the outer ring of the rolling bearing is arranged to have a material weakening in particular two peripheral grooves 5 6 which extend round the rotation axis 1 the first groove 5 is constructed at one side and the second groove at the opposite second side 6 of the bearing receiving member 3 in each case approximately three quarters of the extent of the bearing receiving member 3 in the direction of.