2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59303Let $X$ be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on $X$ which depend only on the norms of images of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of $X$ previously studied in the context of the classical spaces $C(K)$ and $L_1(μ)$.LaTeX2e, 29 pages; Studia Math. (to appear)Functional Analysis46B20; 46B04; 47B38text