Uniformly bounded composition operators between general Lipschitz function normed spaces

Abstract

The notions of uniform boundedness and equidistant uniform boundedness of an operator (both weaker than usual boundedness) are introduced. The main results say that the generator of any uniformly bounded (or equidistantly uniformly bounded) composition Nemytskiĭ operator acting between general Lipschitzian normed function spaces must be affine with respect to the function variable.