G-narrow operators and G-rich subspaces
Open Mathematics (2013)
- Volume: 11, Issue: 9, page 1677-1688
- ISSN: 2391-5455
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topTetiana Ivashyna. "G-narrow operators and G-rich subspaces." Open Mathematics 11.9 (2013): 1677-1688. <http://eudml.org/doc/269043>.
@article{TetianaIvashyna2013,
abstract = {Let X and Y be Banach spaces. An operator G: X → Y is a Daugavet center if ‖G +T‖ = ‖G‖+‖T‖ for every rank-1 operator T. For every Daugavet center G we consider a certain set of operators acting from X, so-called G-narrow operators. We prove that if J is the natural embedding of Y into a Banach space E, then E can be equivalently renormed so that an operator T is (J ○ G)-narrow if and only if T is G-narrow. We study G-rich subspaces of X: Z ⊂ X is called G-rich if the quotient map q: X → X/Z is G-narrow.},
author = {Tetiana Ivashyna},
journal = {Open Mathematics},
keywords = {Daugavet center; Daugavet property; Narrow operator; narrow operators; rich subspaces; Banach spaces},
language = {eng},
number = {9},
pages = {1677-1688},
title = {G-narrow operators and G-rich subspaces},
url = {http://eudml.org/doc/269043},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Tetiana Ivashyna
TI - G-narrow operators and G-rich subspaces
JO - Open Mathematics
PY - 2013
VL - 11
IS - 9
SP - 1677
EP - 1688
AB - Let X and Y be Banach spaces. An operator G: X → Y is a Daugavet center if ‖G +T‖ = ‖G‖+‖T‖ for every rank-1 operator T. For every Daugavet center G we consider a certain set of operators acting from X, so-called G-narrow operators. We prove that if J is the natural embedding of Y into a Banach space E, then E can be equivalently renormed so that an operator T is (J ○ G)-narrow if and only if T is G-narrow. We study G-rich subspaces of X: Z ⊂ X is called G-rich if the quotient map q: X → X/Z is G-narrow.
LA - eng
KW - Daugavet center; Daugavet property; Narrow operator; narrow operators; rich subspaces; Banach spaces
UR - http://eudml.org/doc/269043
ER -
References
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