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Real analytic approximation of Lipschitz functions on Hilbert space and other Banach spaces

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

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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
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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