Abstract
The set M of all concave Marcinkiewicz modulars on [0, 1] is a semigroup with respect to the usual composition of functions. We show that some properties of modulars (which are of importance in interpolation and in general Banach theory) distinguish subsets of M that form ideals of the semigroup. These ideals turn out to be in a natural duality relation, which is also studied. Bibliography: 8 titles.
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