  We develop a new functional-analytic technique for investigating the degree
of noncompactness of an operator defined on a quasinormed space and taking
values in a Marcinkiewicz space. The main result is a general principle from
which it can be derived that such operators are almost always maximally
noncompact in the sense that their ball measure of noncompactness coincides
with their operator norm. We point out specifications of the universal
principle to the case of the identity operator.
