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Higher order Gateaux smooth bump functions on Banach spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
For Г uncountable and p ≥ 1 odd, it is shown ℓp(г) admits no continuous p-times Gateaux differentiable bump function. A space is shown to admit a norm with Hölder derivative on its sphere if it admits a bounded bump function with uniformly directionally Hölder derivative. Some results on smooth approximation are obtained for spaces that admit bounded uniformly Gateaux differentiable bump functions.
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- Research Article
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- Copyright © Australian Mathematical Society 1995
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