Limited operators and differentiability - Bachir, Mohammed (North-Western European Journal of Mathematics, 2023)
We characterize the limited operators by differentiability of convex continuous functions. Given Banach spaces \(Y\) and \(X\) and a linear continuous continuous operator \(T: YX\), we prove that \(T\) is a limited operator if and only if, for every convex continuous function \(f: X R\) and every point \(yY\), \(f° T\) is Fréchet differentiable at \(y Y\) whenever \(f\) is Gâteaux differentiable at \(T(y)X\).