On a characterization of linear operators
Main result: Let \(X\) be a real or complex vector space and let \(B\) be a normed space. The function \(f:X\to B\) is linear if and only if the function \[ (x,y,\lambda)\mapsto f(\lambda x+y)-\lambda f(x)-f(y) \] remains bounded for large \(\lambda\). The author claims that this statement holds also if \(B\) is a locally convex topological vector space.
scientific article; zbMATH DE number 897185