2016/02/12 by Mohammed Bachir, Bachir, Mohammed
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Optimization and Variational Analysis #math.FA
paper · pdf · doi:10.48550/arxiv.1602.04173
arxiv created 2016/02/12 · openalex publication_date 2016/02/12 · arxiv updated 2016/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize the limited operators by differentiability of convex continuous functions. Given Banach spaces Y and X and a linear continuous operator T: Y \longrightarrow X, we prove that T is a limited operator if and only if, for every convex continuous function f: X \longrightarrow \R and every point y∈ Y, f∘ T is Fréchet differentiable at y∈ Y whenever f is Gâteaux differentiable at T(y)∈ X.