Operator calculus on ultrasmooth vectors - Lopushansky , О. V. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
A general method of constructing functions of unbounded operators acting in Banach spaces is set forth. It is based on equipping the initial space with invariant subspaces of ultradifferential vectors of a specified operator and describing the spectral properties of the initial space in the topological algebras which thereby arise.