Sums of SCD sets and their applications to SCD operators and narrow operators

• Autorzy: Vladimir Kadets , Varvara Shepelska
• Języki publikacji: EN

Abstrakty

EN

We answer two open questions concerning the recently introduced notions of slicely countably determined (SCD) sets and SCD operators in Banach spaces. An application to narrow operators in spaces with the Daugavet property is given.

Słowa kluczowe

EN

Daugavet equation; Radon-Nikodým property; Containing of ℓ1; Narrow operators

Kategorie tematyczne

• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 46B20: Geometry and structure of normed linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 129-134

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Vladimir Kadets

• Kharkov National University

autor

Varvara Shepelska

• Kharkov National University

Bibliografia

• [1] Avilés A., Kadets V., Martín M., Merí J., Shepelska V., Slicely countably determined Banach spaces, C. R. Acad. Sci. Paris, Ser. I, 2009, 347, 1277–1280
• [2] Avilés A., Kadets V., Martín M., Merí J., Shepelska V., Slicely countably determined Banach spaces. Applications to the Daugavet and the alternative Daugavet equations, Trans. Amer. Math. Soc., to appear
• [3] Kadets V., Martín M., Payá R., Recent progres and open questions on the numerical index of Banach spaces, Rev. R. Acad. Cien. SerieA. Mat., 2006, 100(1–2), 155–182
• [4] Kadets V. M., Shvidkoy R. V., Sirotkin G. G., Werner D., Banach spaces with the Daugavet property, Trans. Amer. Math. Soc., 2000, 352, 855–873 http://dx.doi.org/10.1090/S0002-9947-99-02377-6
• [5] Kadets V. M., Shvidkoy R. V., Werner D., Narrow operators and rich subspaces of Banach spaces with the Daugavet property, Studia Math., 2001, 147, 269–298 http://dx.doi.org/10.4064/sm147-3-5

Identyfikatory

DOI

10.2478/s11533-009-0075-7