# 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
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