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

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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
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 Aug 2018 10:46

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