  Majorization uncertainty relations are derived for arbitrary quantum
operations acting on a finite-dimensional space. The basic idea is to consider
submatrices of block matrices comprised of the corresponding Kraus operators.
This is an extension of the previous formulation, which deals with submatrices
of a unitary matrix relating orthogonal bases in which measurements are
performed. Two classes of majorization relations are considered: one related to
tensor product of probability vectors and another one related to their direct
sum. We explicitly discuss an example of a pair of one-qubit operations, each
of them represented by two Kraus operators. In the particular case of quantum
maps describing orthogonal measurements the presented formulation reduces to
earlier results derived for measurements in orthogonal bases. The presented
approach allows us also to bound the entropy characterizing results of a single
generalized measurement.
