The approximation of fractional powers of a closed operator

Source abstract

This paper provides a unified approach to some perturbation problems recently considered by the author in joint work with S. Kantorovitz. The key result is that the semigroup of unbounded operators $\{J^{\alpha}\}$ formed by the fractional powers of a closed operator $J$ can be approximated in a canonical way by a certain family of bounded semigroups.