Non p-norm approximated Groups

It was shown in a previous work of the first-named author with De Chiffre, Glebsky and Thom that there exists a finitely presented group which cannot be approximated by almost-homomorphisms to the unitary groups U(n) equipped with the Frobenius norms (a.k.a. as L 2 norm, or the Schatten-2-norm). In his ICM18 lecture, Andreas Thom asks if this result can be extended to general Schatten- p -norms. We show that this is indeed the case for 1 < p < ∞ .