Subspaces of Banach spaces with big slices

Preprint, Other literature type English OPEN
Guerrero, Julio Becerra; López-Pérez, Ginés; Zoca, Abraham Rueda;

We study when diameter $2$ properties can be inherited by subspaces. We obtain that the slice diameter $2$ property (resp., the diameter $2$ property, strong diameter $2$ property) passes from a Banach space $X$ to a subspace $Y$ whenever $X/Y$ is finite-dimensional and... View more
  • References (9)

    [1] J. Becerra Guerrero, G. L´opez-P´erez and Abraham Rueda Zoca, Octahedral norms and convex combination of slices in Banach spaces, J. Func. Anal. 266 (4) (2014), 2424-2436.

    [2] J. Becerra Guerrero, G. L´opez-P´erez and Abraham Rueda Zoca, Extreme differences between weakly open subsets and convex combinations of slices in Banach spaces. To appear in Adv. Math.

    [3] J. Bourgain. La propri´et´e de Radon-Nikodym. Publications de l'Universit´e Pierre et Marie Curie. 36, Paris 1979.

    [4] R. Deville, G. Godefroy, V. Zizler. Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Applied Math. 64, 1993.

    [5] N. Ghoussoub, G. Godefroy, B. Maurey, W. Schachermayer, Some topological and geometrical structures in Banach spaces, Memoirs of Amer. Math. Soc. (378) 70 1987.

    [6] R. Haller, J. Langemets, and M. Po˜ldvere, On duality of diameter 2 properties. To appear in J. Conv. Anal.

    [7] W. Schachermayer. The Radon-Nikodym property and the Krein Milman property are equivalent for strongly regular sets. Trans. Amer. Math. Soc. 303 (2) (1987), 673-687.

    [8] W. Schachermayer, A. Sersouri and E. Werner, Moduli of nondentability and the Radon-Nikod´ym property in Banach spaces, Israel J. Math. 65 (3) (1989), 225-257.

    [9] R.V. Shvydkoy, Geometric aspects of the Daugavet property, J. Funct. Anal. 176 (2000), 198-212. Universidad de Granada, Facultad de Ciencias. Departamento de Ana´lisis Matema´tico, 18071-Granada (Spain) E-mail address:,,

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