Higher order Gateaux smooth bump functions on Banach spaces
1995 ◽
Vol 51
(2)
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pp. 291-300
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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.
2016 ◽
Vol 214
(2)
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pp. 553-581
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1997 ◽
Vol 40
(1)
◽
pp. 88-102
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Keyword(s):
2013 ◽
Vol 21
(3)
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2006 ◽
Vol 313
(2)
◽
pp. 572-580
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1999 ◽
Vol 5
(3)
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pp. 651-662