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 < ∞ .

中文翻译：

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非 p 范数近似组

在第一作者与 De Chiffre、Glebsky 和 ​​Thom 的先前工作中表明，存在一个有限呈现群，该群不能通过几乎同态逼近配备 Frobenius 范数（又名）的酉群 U(n)作为 L 2 范数，或 Schatten-2-范数）。在他的 ICM18 演讲中，Andreas Thom 问这个结果是否可以扩展到一般 Schatten-p 范数。我们证明 1 < p < ∞ 确实是这种情况。