Daniel Azagra, Juan Ferrera, Javier Gómez-Gil, Carlos Mudarra
Published 2018-11-13Version 1
Let $E$ be an arbitrary subset of a Banach space $X$, $f: E \rightarrow \mathbb{R}$ be a function, and $G:E \rightrightarrows X^*$ be a set-valued mapping. We give necessary and sufficient conditions on $f, G$ for the existence of a continuous convex extension $F: X \rightarrow \mathbb{R} $ of $f$ such that the subdifferential $\partial F$ of $F$ coincides with $G$ on $E.$
Embedding $\ell_{\infty}$ into the space of all Operators on Certain Banach Spaces
An interplay between the weak form of Peano's theorem and structural aspects of Banach spaces
Existence of zeros for operators taking their values in the dual of a Banach space
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