Recently, a complete characterization of connected Lie groups with the Approximation Property was given. The proof used the newly introduced property(T*). We present here a short proof of the same result avoiding the use of property (T*). Using property (T*), however, the characterization is extended to almost connected locally compact groups. We end with some remarks about the difficulty of going beyond the almost connected case. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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