### Impacto

Azagra Rueda, Daniel and Fry, Robb and Keener , L.
(2012)
*Real analytic approximation of Lipschitz functions on Hilbert space and other Banach spaces.*
Journal of Functional Analysis , 262
(1).
pp. 124-166.
ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123611003387

## Abstract

Let X be a separable Banach space with a separating polynomial. We show that there exists C >= 1 (depending only on X) such that for every Lipschitz function f : X -> R, and every epsilon > 0, there exists a Lipschitz, real analytic function g : X -> R such that vertical bar f (x) - g(x)vertical bar <= epsilon e and Lip(g) <= C Lip(f). This result is new even in the case when X is a Hilbert space. Furthermore, in the Hilbertian case we also show that C can be assumed to be any number greater than I.

Item Type: | Article |
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Uncontrolled Keywords: | Real analytic; Approximation; Lipschitz function; Banach space;Differentiable Functions; Polynomials; Derivatives; C(0); Maps |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 14741 |

Deposited On: | 17 Apr 2012 10:39 |

Last Modified: | 06 Feb 2014 10:07 |

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