Extremely non-complex Banach spaces

• Autorzy: Miguel Martín , Javier Merí
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Banach space; Complex structure; Daugavet equation; Extremely non-complex; Numerical index; Diameter of slices

Kategorie tematyczne

• 46B04: Isometric theory of Banach spaces
• 47A99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 797-802

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

Miguel Martín

• Universidad de Granada

autor

Javier Merí

• Universidad de Granada

Bibliografia

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• [2] Kadets V.M., Some remarks concerning the Daugavet equation, Quaest. Math., 1996, 19(1–2), 225–235 http://dx.doi.org/10.1080/16073606.1996.9631836
• [3] Kadets V., Katkova O., Martín M., Vishnyakova A., Convexity around the unit of a Banach algebra, Serdica Math. J., 2008, 34(3), 619–628
• [4] Kadets V., Martín M., Merí J., Norm equalities for operators, Indiana Univ. Math. J., 2007, 56(5), 2385–2411 http://dx.doi.org/10.1512/iumj.2007.56.3046
• [5] Kadets V.M., Shvidkoy R.V., Sirotkin G.G., Werner D., Banach spaces with the Daugavet property, Trans. Amer. Math. Soc., 2000, 352(2), 855–873 http://dx.doi.org/10.1090/S0002-9947-99-02377-6
• [6] Koszmider P., Banach spaces of continuous functions with few operators, Math. Ann., 2004, 330(1), 151–183 http://dx.doi.org/10.1007/s00208-004-0544-z
• [7] Koszmider P., Martín M., Merí J., Extremely non-complex C(K) spaces, J. Math. Anal. Appl., 2009, 350(2), 601–615 http://dx.doi.org/10.1016/j.jmaa.2008.04.021
• [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
• [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
• [10] Megginson R.E., An Introduction to Banach Space Theory, Grad. Texts in Math., 183, Springer, New York, 1998
• [11] Oikhberg T., Some properties related to the Daugavet property, In: Banach Spaces and their Applications in Analysis, Walter de Gruyter, Berlin, 2007, 399–401

Identyfikatory

DOI

10.2478/s11533-011-0040-0