  Sukochev and Zanin resolved an open problem due to B. Simon concerning
optimal constants in H\"older inequality for the weak Schatten classes of
compact operators. In this note we observe that these constants, by introducing
the modified weak Schatten quasi-norms, can be renormalised so that the
original Simon's conjecture (with optimal constant 1) does hold. We also
provide an unexpectedly simple proof for the modified H\"older inequality and
its sharpness.
