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 L₁(μ).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-3-5,
author = {Vladimir M. Kadets and Roman V. Shvidkoy and Dirk Werner},
title = {Narrow operators and rich subspaces of Banach spaces with the Daugavet property},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {269-298},
zbl = {0986.46010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-3-5}
}
Vladimir M. Kadets; Roman V. Shvidkoy; Dirk Werner. Narrow operators and rich subspaces of Banach spaces with the Daugavet property. Studia Mathematica, Tome 147 (2001) pp. 269-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-3-5/