Publication: C1-fine approximation of functions on Banach spaces with unconditional basis
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2005-03
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Oxford University Press
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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.