Journal Article

<i>C</i><sup>1</sup>-fine approximation of functions on Banach spaces with unconditional basis

Daniel Azagra, Javier Gómez Gil, Jesús A. Jaramillo, Mauricio Lovo and Robb Fry

in The Quarterly Journal of Mathematics

Volume 56, issue 1, pages 13-20
Published in print March 2005 | ISSN: 0033-5606
Published online March 2005 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/hah020
C1-fine approximation of functions on Banach spaces with unconditional basis

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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 : XY such that ‖fg‖ ≤ ε and ‖fg‖ ≤ ε.

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Subjects: Pure Mathematics

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