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

@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 -