Asymptotic geometry of Banach spaces and uniform quotient maps

Dilworth, S.; Kutzarova, Denka; Lancien, G.; Randrianarivony, N.

doi:10.1090/S0002-9939-2014-12001-6

Asymptotic geometry of Banach spaces and uniform quotient maps
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by S. J. Dilworth, Denka Kutzarova, G. Lancien and N. L. Randrianarivony PDF

Proc. Amer. Math. Soc. 142 (2014), 2747-2762

Abstract:

Recently, Lima and Randrianarivony pointed out the role of the property $(\beta )$ of Rolewicz in nonlinear quotient problems and answered a ten-year-old question of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. In the present paper, we prove that the modulus of asymptotic uniform smoothness of the range space of a uniform quotient map can be compared with the modulus of $(\beta )$ of the domain space. We also provide conditions under which this comparison can be improved.

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