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Infinite-dimensional analog of Zigel's theorem

✍ Scribed by L. V. Novikova


Publisher
Springer US
Year
1982
Tongue
English
Weight
218 KB
Volume
16
Category
Article
ISSN
0016-2663

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We prove the following new characterization of C p (Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space X has a C p smooth (Lipschitz) bump function if and only if it has another C p smooth (Lipschitz) bump function f such that its derivative does not vanish at any point in