Smooth extensions of functions on separable Banach spaces
D. Azagra, R. Fry, L. Keener

TL;DR
This paper proves that any $C^{1}$-smooth function defined on a closed subspace of a Banach space with a separable dual can be extended to a $C^{1}$-smooth function on the entire space.
Contribution
It establishes the existence of $C^{1}$ smooth extensions for functions on subspaces of Banach spaces with separable duals, generalizing previous extension results.
Findings
Existence of $C^{1}$ extensions for functions on subspaces
Extension applies to Banach spaces with separable duals
Provides a constructive method for smooth extensions
Abstract
Let be a Banach space with a separable dual . Let be a closed subspace, and a -smooth function. Then we show there is a extension of to .
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Harmonic Analysis Research · Holomorphic and Operator Theory
