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 ′| < ....
Saved in:
| Published in: | The Bulletin of the London Mathematical Society Vol. 43; no. 5; pp. 953 - 964 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford University Press
01.10.2011
|
| ISSN: | 0024-6093, 1469-2120 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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
′| < . |
|---|---|
| Bibliography: | 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 |