Principles of functional analysis in scales of spaces: Hahn-Banach theorem, Banach theorem on homomorphisms, and theorems on open mappings and closed graphs

The Hahn-Banach theorem, the Banach theorem on homomorphisms, and theorems on open mappings and closed graphs are transferred to functionals and operators acting in inductive scales of spaces. The applications to operators acting in inductive limits and dual spaces are considered. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 5, pp. 153–173, 2005.