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

Vladimir M. Kadets, Roman V. Shvidkoy, and Dirk Werner. "Narrow operators and rich subspaces of Banach spaces with the Daugavet property." Studia Mathematica 147.3 (2001): 269-298. <http://eudml.org/doc/284633>.

@article{VladimirM2001,
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 L₁(μ).},
author = {Vladimir M. Kadets, Roman V. Shvidkoy, Dirk Werner},
journal = {Studia Mathematica},
keywords = {Daugavet property; Daugavet equation; rich subspace; narrow operator; Radon-Nikodým operators},
language = {eng},
number = {3},
pages = {269-298},
title = {Narrow operators and rich subspaces of Banach spaces with the Daugavet property},
url = {http://eudml.org/doc/284633},
volume = {147},
year = {2001},
}

TY - JOUR
AU - Vladimir M. Kadets
AU - Roman V. Shvidkoy
AU - Dirk Werner
TI - Narrow operators and rich subspaces of Banach spaces with the Daugavet property
JO - Studia Mathematica
PY - 2001
VL - 147
IS - 3
SP - 269
EP - 298
AB - 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).
LA - eng
KW - Daugavet property; Daugavet equation; rich subspace; narrow operator; Radon-Nikodým operators
UR - http://eudml.org/doc/284633
ER -