Narrow operators and rich subspaces of Banach spaces with the Daugavet property

Details Narrow operators and rich subspaces of Banach spaces with the Daugavet property Narrow operators and rich subspaces of Banach spaces with the Daugavet property

2000-05-30

arxiv.org/abs/math/0005278v2

Studia Math. 147 (2001), 269-298.

Mathematics

Functional Analysis

LaTeX2e, 29 pages; Studia Math. (to appear)

Scientific paper

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 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 $L_1(\mu)$.

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