| In this paper we strudy the so-called atomic and coatomic operators introduced in [7] ideal function spaces. In particular, we discover characteristic properties of such operators, which can serve as their new definitions. These properties are intrinsic in the sense that they are independent of a particular σ-homomorphism of the underlying σ-algebrae and are based on purely measure-theoretic notions of memory and comemory of an operator, which are also studied in details in the paper. We also prove some new results on analytic properties of atomic, coatomic and local operators. For the reader's convenience some of the known results regarding such operators that are exploited in the present paper are also provided without proofs. In the last section, we show that the study of strong periodic (in distribution) solutions to a stochastic functional differential equation can be put, under rather general assumptions, into the framework of atomic operators. This result can serve as an additional strong motivation for introducing and studying atomic and coatomic operators in their most general form.
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