| Résume | A group is called strongly Ulam-stable if near an almost representation on a Hilbert space (meaning that the homomorphism equality holds up to some error in the norm) there is a close actual unitary representation. Kazhan showed that all amenable groups are strongly Ulam-stable. In the onter direction the best known result, by Burger, Ozawa and Thow, was that every group containing a non-abelian free group is nos strongly Ulam-stable. I will show that lamplighters over non-amenable groups are not strongly Uam-stable.
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