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On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces

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Jiménez Sevilla, María del Mar and Sánchez González, Luis (2013) On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces. Mathematische Annalen, 355 (4). pp. 1201-1219. ISSN 0025-5831

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Official URL: http://link.springer.com/content/pdf/10.1007%2Fs00208-012-0814-0.pdf


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Abstract

Let and be Banach spaces, a closed subset of and a mapping . We give necessary and sufficient conditions to obtain a smooth mapping such that , when either (i) and are Hilbert spaces and is separable, or (ii) is separable and is an absolute Lipschitz retract, or (iii) and with , or (iv) and with , where is any separable Banach space with a -finite measure space.


Item Type:Article
Uncontrolled Keywords:Lipschitz functions; approximations; subspaces
Subjects:Sciences > Mathematics
ID Code:21227
Deposited On:06 May 2013 11:22
Last Modified:27 Jul 2018 08:02

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