  In this paper, we first provide three general norm inequalities, which are
used to give new uncertainty relations of any finite observables and quantum
channels via metric-adjusted skew information. The results are applicable to
its special cases as Wigner-Yanase-Dyson skew information. In quantifying the
uncertainty of channels, we discuss two types of lower bounds and compare the
tightness between them, meanwhile, a tight lower bound is given. The
uncertainty relations obtained by us are stronger than the existing ones. To
illustrate our results, we give several specific examples.
