TY - JOUR
T1 - Asymptotic geometry of banach spaces and uniform quotient maps
AU - Dilworth, S. J.
AU - Kutzarova, Denka
AU - Lancien, G.
AU - Randrianarivony, N. L.
N1 - Publisher Copyright:
© 2014, By the authors.
PY - 2014/8/1
Y1 - 2014/8/1
N2 - Recently, Lima and Randrianarivony pointed out the role of the property (β) of Rolewicz in nonlinear quotient problems and answered a tenyear-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 (β) of the domain space. We also provide conditions under which this comparison can be improved.
AB - Recently, Lima and Randrianarivony pointed out the role of the property (β) of Rolewicz in nonlinear quotient problems and answered a tenyear-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 (β) of the domain space. We also provide conditions under which this comparison can be improved.
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U2 - 10.1090/S0002-9939-2014-12001-6
DO - 10.1090/S0002-9939-2014-12001-6
M3 - Article
AN - SCOPUS:84924787958
SN - 0002-9939
VL - 142
SP - 2747
EP - 2762
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 8
ER -