Narrow operators and rich subspaces of Banach spaces with the Daugavet property
Volume 147 / 2001
Studia Mathematica 147 (2001), 269-298
MSC: Primary 46B20; Secondary 46B04, 47B38.
DOI: 10.4064/sm147-3-5
Abstract
Let $X$ 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 the 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 spaces $X$ with the Daugavet property previously studied in the context of the classical spaces $C(K)$ and $L_{1}(\mu )$.
