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C1-fine approximation of functions on Banach spaces with unconditional basis

Azagra Rueda, Daniel and Gómez Gil, Javier and Fry, Robb and Lovo, Mauricio and Jaramillo Aguado, Jesús Ángel (2005) C1-fine approximation of functions on Banach spaces with unconditional basis. Quaterly Journal of Mathematics, 56 (1). pp. 13-20. ISSN 0033-5606

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Abstract

We show that if X is a Banach space having an unconditional basis and a Cp-smooth Lipschitz bump function, then for every C1-smooth function f from X into a Banach space Y, and for every continuous function ε : X → (0, ∞), there exists a Cp-smooth function g : X → Y such that ‖f − g‖ ≤ ε and ‖f′ − g′‖ ≤ ε.


Item Type:Article
Uncontrolled Keywords:Smooth bumps; Fine approximation
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:12356
Deposited On:07 Mar 2011 11:23
Last Modified:06 Feb 2014 09:23

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