Understanding the launching, acceleration, and collimation of jets powered by active galactic nuclei remains an outstanding problem in relativistic astrophysics. This is partly because observational tests of jet formation models suffer from the limited angular resolution of ground-based very long baseline interferometry that has thus far been able to probe the transverse jet structure in the acceleration and collimation zone of only two sources. Here we report radio interferometric observations of 3C 84 (NGC 1275), the central galaxy of the Perseus cluster, made with an array including the orbiting radio telescope of the RadioAstron mission. The obtained image transversely resolves the edge-brightened jet in 3C 84 only 30 microarcseconds from the core, which is ten times closer to the central engine than what has been possible in previous ground-based observations, and it allows us to measure the jet collimation profile from ~ 100 to ~10000 gravitational radii from the black hole. The previously found, almost cylindrical jet profile on scales larger than a few thousand r_g is now seen to continue at least down to a few hundred r_g from the black hole and we find a broad jet with a transverse radius larger than about 250 r_g at only 350 r_g from the core. If the bright outer jet layer is launched by the black hole ergosphere, it has to rapidly expand laterally on scales smaller than 100 r_g. If this is not the case, then this jet sheath is likely launched from the accretion disk.
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