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.
@article{bwmeta1.element.doi-10_2478_s11533-011-0040-0,
author = {Miguel Mart\'\i n and Javier Mer\'\i },
title = {Extremely non-complex Banach spaces},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {797-802},
zbl = {1242.46015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0040-0}
}
Miguel Martín; Javier Merí. Extremely non-complex Banach spaces. Open Mathematics, Tome 9 (2011) pp. 797-802. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0040-0/
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