  Which matrix norms induce proper measures for quantifying quantum coherence?
We study this problem for two important classes of norms and show that (i)
coherence measures cannot be induced by any unitary similarity invariant norm,
and (ii) the $\ell_{q,p}$-norm induces a coherence measure if and only if $q=1$
and $1 \leq p \leq 2$, thus giving a new class of coherence measures with
simple closed forms that are easy to compute. These results extend and unify
previously known facts about norm-induced coherence measures, and lead to a
broader framework for understanding what functionals can be coherence measures.
