C1-fine approximation of functions on Banach spaces with unconditional basis
Copyright policy )C1-fine approximation of functions on Banach spaces with unconditional basis
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.
Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Geometry and structure of normed linear spaces, Isomorphic theory (including renorming) of Banach spaces, Smooth bumps, fine approximation, Fine approximation, smooth bumps, 517.98, Análisis funcional y teoría de operadores
Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Geometry and structure of normed linear spaces, Isomorphic theory (including renorming) of Banach spaces, Smooth bumps, fine approximation, Fine approximation, smooth bumps, 517.98, Análisis funcional y teoría de operadores
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