Sums of SCD sets and their applications to SCD operators and narrow operators
Vladimir Kadets; Varvara Shepelska
Open Mathematics (2010)
- Volume: 8, Issue: 1, page 129-134
- ISSN: 2391-5455
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topVladimir Kadets, and Varvara Shepelska. "Sums of SCD sets and their applications to SCD operators and narrow operators." Open Mathematics 8.1 (2010): 129-134. <http://eudml.org/doc/269287>.
@article{VladimirKadets2010,
abstract = {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.},
author = {Vladimir Kadets, Varvara Shepelska},
journal = {Open Mathematics},
keywords = {Daugavet equation; Radon-Nikodým property; Containing of ℓ1; Narrow operators; Containing of },
language = {eng},
number = {1},
pages = {129-134},
title = {Sums of SCD sets and their applications to SCD operators and narrow operators},
url = {http://eudml.org/doc/269287},
volume = {8},
year = {2010},
}
TY - JOUR
AU - Vladimir Kadets
AU - Varvara Shepelska
TI - Sums of SCD sets and their applications to SCD operators and narrow operators
JO - Open Mathematics
PY - 2010
VL - 8
IS - 1
SP - 129
EP - 134
AB - 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.
LA - eng
KW - Daugavet equation; Radon-Nikodým property; Containing of ℓ1; Narrow operators; Containing of
UR - http://eudml.org/doc/269287
ER -
References
top- [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 Zbl1187.46007
- [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 Zbl1187.46007
- [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 Zbl1111.46007
- [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 Zbl0938.46016
- [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 Zbl0986.46010
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