G-narrow operators and G-rich subspaces

• Autorzy: Tetiana Ivashyna
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Daugavet center; Daugavet property; Narrow operator

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B04: Isometric theory of Banach spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 9
• Strony: 1677-1688

Daty

wydano

2013-09-01

online

2013-06-28

Twórcy

autor

Tetiana Ivashyna

• Vasyl N. Karazin Kharkiv National University

Bibliografia

• [1] Bosenko T.V., Strong Daugavet operators and narrow operators with respect to Daugavet centers, Vestnik Khar’kov. Univ., 2010, 931(62), 5–19
• [2] Bosenko T., Kadets V., Daugavet centers, Zh. Mat. Fiz. Anal. Geom., 2010, 6(1), 3–20
• [3] Kadets M.I., Kadets V.M., Series in Banach Spaces, Oper. Theory Adv. Appl., 94, Birkhäuser, Basel, 1997
• [4] Kadets V.M., Some remarks concerning the Daugavet equation, Quaestiones Math., 1996, 19(1–2), 225–235 http://dx.doi.org/10.1080/16073606.1996.9631836
• [5] Kadets V.M., Popov M.M., Some stability theorems on narrow operators acting on L1 and C(K), Mat. Fiz. Anal. Geom., 2003, 10(1), 49–60
• [6] Kadets V.M., Shvidkoy R.V., Sirotkin G.G., Werner D., Banach spaces with the Daugavet property, Trans. Amer. Math. Soc., 2000, 352(2), 855–873 http://dx.doi.org/10.1090/S0002-9947-99-02377-6
• [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

Identyfikatory

DOI

10.2478/s11533-013-0266-0