Extremely non-complex Banach spaces
Open Mathematics (2011)
- Volume: 9, Issue: 4, page 797-802
- ISSN: 2391-5455
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topMiguel Martín, and Javier Merí. "Extremely non-complex Banach spaces." Open Mathematics 9.4 (2011): 797-802. <http://eudml.org/doc/269605>.
@article{MiguelMartín2011,
abstract = {A Banach space X is said to be an extremely non-complex space if the norm equality ∥Id +T 2∥ = 1+∥T 2∥ holds for every bounded linear operator T on X. We show that every extremely non-complex Banach space has positive numerical index, it does not have an unconditional basis and that the infimum of diameters of the slices of its unit ball is positive.},
author = {Miguel Martín, Javier Merí},
journal = {Open Mathematics},
keywords = {Banach space; Complex structure; Daugavet equation; Extremely non-complex; Numerical index; Diameter of slices; complex structure; extremely non-complex Banach space; numerical index; diameter of slices},
language = {eng},
number = {4},
pages = {797-802},
title = {Extremely non-complex Banach spaces},
url = {http://eudml.org/doc/269605},
volume = {9},
year = {2011},
}
TY - JOUR
AU - Miguel Martín
AU - Javier Merí
TI - Extremely non-complex Banach spaces
JO - Open Mathematics
PY - 2011
VL - 9
IS - 4
SP - 797
EP - 802
AB - A Banach space X is said to be an extremely non-complex space if the norm equality ∥Id +T 2∥ = 1+∥T 2∥ holds for every bounded linear operator T on X. We show that every extremely non-complex Banach space has positive numerical index, it does not have an unconditional basis and that the infimum of diameters of the slices of its unit ball is positive.
LA - eng
KW - Banach space; Complex structure; Daugavet equation; Extremely non-complex; Numerical index; Diameter of slices; complex structure; extremely non-complex Banach space; numerical index; diameter of slices
UR - http://eudml.org/doc/269605
ER -
References
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- [8] Koszmider P., Martín M., Merí J., Isometries on extremely non-complex C(K) spaces, J. Inst. Math. Jussieu, 2011, 10(2), 325–348 http://dx.doi.org/10.1017/S1474748010000204 Zbl1221.46012
- [9] Martín M., Oikhberg T., An alternative Daugavet property, J. Math. Anal. Appl., 2004, 294(1), 158–180 http://dx.doi.org/10.1016/j.jmaa.2004.02.006 Zbl1054.46010
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