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Some questions about rotundity and renormings in Banach spaces

  • A. Aizpuru (a1) and F. J. Garcia-Pacheco (a1)

Abstract

In this paper, we show some results involving classical geometric concepts. For example, we characterize rotundity and Efimov-Stechkin property by mean of faces of the unit ball. Also, we prove that every almost locally uniformly rotund Banach space is locally uniformly rotund if its norm is Fréchet differentiable. Finally, we also provide some theorems in which we characterize the (strongly) exposed points of the unit ball using renormings.

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References

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[1]Banas, J., ‘On drop property and nearly uniformly smooth Banach spaces’, Nonlinear Anal. 14 (1990), 927933.
[2]Bandyopadhyay, P., Huang, D., Lin, B.-L. and Troyanski, S. L., ‘Some generalizations of locally uniform rotundity’, J. Math. Anal. Appl. 252 (2000), 906916.
[3]Bandyopadhyay, P. and Lin, B.-L., ‘Some properties related to nested sequence of balls in Banach spaces’, Taiwanese J. Math. 5 (2001), 1934.
[4]Giles, J. R., ‘Strong differentiability of the norm and rotundity of the dual’, J. Austral. Math. Soc. 26 (1978), 302308.
[5]Megginson, R. E., An introduction to Banach space theory (Springer, New York, 1998).
[6]Singer, I., ‘Some remarks on approximative compactness’, Rev. Roumaine Math. Pures Appl. 9 (1964), 167177.
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Some questions about rotundity and renormings in Banach spaces

  • A. Aizpuru (a1) and F. J. Garcia-Pacheco (a1)

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