# 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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- [7] Kadets V.M., Shvidkoy R.V., Werner D., Narrow operators and rich subspaces of Banach spaces with the Daugavet property, Studia Math., 2001, 147(3), 269–298 http://dx.doi.org/10.4064/sm147-3-5 Zbl0986.46010

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