Approximation of functions and their derivatives by analytic maps on certain Banach spaces
Let X be a separable Banach space that admits a separating polynomial; in particular, let X be a separable Hilbert space. Let f: X → be bounded and Lipschitz, with uniformly continuous derivative. Then, for each > 0, there exists an analytic function g: X → with | g−f| < and | g ′−f ′| < ....
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| Vydáno v: | The Bulletin of the London Mathematical Society Ročník 43; číslo 5; s. 953 - 964 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Oxford University Press
01.10.2011
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| ISSN: | 0024-6093, 1469-2120 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Let X be a separable Banach space that admits a separating polynomial; in particular, let X be a separable Hilbert space. Let f: X → be bounded and Lipschitz, with uniformly continuous derivative. Then, for each > 0, there exists an analytic function g: X → with | g−f| < and | g
′−f
′| < . |
|---|---|
| Bibliografie: | 2010 Mathematics Subject Classification The second named author was partly supported by NSERC (Canada). 46B20 (primary). |
| ISSN: | 0024-6093 1469-2120 |
| DOI: | 10.1112/blms/bdr032 |