  Building upon Bennett's and Grosse-Erdmann's ideas falling under the
conceptual umbrella of factorization of inequalities, we propose a unified
approach towards the structure of certain Banach ideal spaces defined in terms
of the least decreasing majorant. The key to our results, and, it seems, the
main novelty in general, is the synthesis of discretization process, usually
called the blocking technique, along with some tools from the interpolation
theory. This blend allows us to obtain an abstract versions of several
remarkable results proposed by Bennett and to show certain phenomena in new,
somehow more complete perspective. Furthermore, with the help of technology we
have developed, we re-prove and sometimes also improve many more recent results
belonging to this circle of ideas.
