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On the peano theorem in infinite-dimensional spaces

✍ Scribed by M. I. Kamenskii


Publisher
SP MAIK Nauka/Interperiodica
Year
1972
Tongue
English
Weight
268 KB
Volume
11
Category
Article
ISSN
0001-4346

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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