Azagra Rueda, Daniel and Gómez Gil, Javier and Fry, Robb and Lovo, Mauricio and Jaramillo Aguado, Jesús Ángel (2005) C1-fine approximation of functions on Banach spaces with unconditional basis. Quaterly Journal of Mathematics, 56 (1). pp. 13-20. ISSN 0033-5606
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Official URL: http://qjmath.oxfordjournals.org/
Abstract
We show that if X is a Banach space having an unconditional basis and a Cp-smooth Lipschitz bump function, then for every C1-smooth function f from X into a Banach space Y, and for every continuous function ε : X → (0, ∞), there exists a Cp-smooth function g : X → Y such that ‖f − g‖ ≤ ε and ‖f′ − g′‖ ≤ ε.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Smooth bumps; Fine approximation |
| Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |
| ID Code: | 12356 |
| Deposited On: | 07 Mar 2011 12:23 |
| Last Modified: | 14 May 2013 16:39 |
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