Abstract
In this note we prove that every Banach space that is representable in a compact Hausdorff topological space in the sense of (J Funct Anal 254:2294–2302, 2008) has the polynomial Daugavet property. As an application we provide new examples of Banach spaces enjoying the polynomial Daugavet property.
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Y. Abramovich and C. Aliprantis, An Invitation to Operator Theory, Graduate Texts in Math., 50, Amer. Math. Soc., Providence, RI, 2002.
Y. Abramovich and C. Aliprantis, Problems in Operator Theory, Graduate Texts in Math., 51, Amer. Math. Soc., Providence, RI, 2002.
Acosta M. D., Kamińska A., Mastyło M.: The Daugavet property in rearrangement invariant spaces. Trans. Amer. Math. Soc. 367, 4061–4078 (2015)
Becerra Guerrero J., Rodríguez-Palacios A.: Banach spaces with the Daugavet property, and the centralizer. J. Funct. Anal. 254, 2294–2302 (2008)
E. Behrends, M-Structure and the Banach-Stone Theorem, Lecture Notes in Math., vol. 736, Springer, Berlin, 1979, x+217 pp.
Choi Y. S., García D., Maestre M., Martín M.: The Daugavet equation for polynomials. Studia Math. 178, 63–82 (2007)
Choi Y. S., García D., Maestre M., Martín M.: The polynomial numerical index for some complex vector-valued function spaces. Q. J. Math. 59, 455–474 (2008)
Daugavet I. K.: On a property of completely continuous operators in the space C. Uspekhi Mat. Nauk 18, 157–158 (1963) (Russian)
J. Diestel, Sequences and Series in Banach Spaces, Graduate Texts in Mathematics, 92, Springer-Verlag, New York, 1984.
Dineen S.: Complex Analysis on Infinite Dimensional Spaces. Springer-Verlag, London (1999)
Kadets V., Martín M., Merí J., Werner D.: Lipschitz slices and the Daugavet equation for Lipschitz operators. Proc. Amer. Math. Soc. 143, 5281–5292 (2015)
Kadets V. M., Shvidkoy R. V., Sirotkin G. G., Werner D.: Banach spaces with the Daugavet property. Trans. Amer. Math. Soc. 352, 855–873 (2000)
Martín M., Merí J., Popov M.: The polynomial Daugavet property for atomless \({L_1(\mu)}\)-spaces. Arch. Math. 94, 383–389 (2010)
J. Mujica, Complex Analysis in Banach Spaces, Dover Publ. Inc., Mineola, New York, 2010.
Santos E. R.: An alternative polynomial Daugavet property. Studia Math. 224, 265–276 (2014)
Santos E. R.: The Daugavet equation for polynomials on C*-algebras. J. Math. Anal. Appl. 409, 598–606 (2014)
Werner D.: Recent progress on the Daugavet property: Irish Math. Soc. Bull. 46, 77–97 (2001)
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Supported by CNPq Grant 305958/2014-3 and Fapemig Grant PPM-00490-15. Supported by Fapemig Grant APQ-00522-14.
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Botelho, G., Santos, E.R. Representable spaces have the polynomial Daugavet property. Arch. Math. 107, 37–42 (2016). https://doi.org/10.1007/s00013-016-0914-2
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DOI: https://doi.org/10.1007/s00013-016-0914-2