A note on the convergence of linear semi-groups of class (1,A)
Nazar Hussein Abdelaziz · Hokkaido Mathematical Journal · 1989
In the present paper we prove a Trotter-Kato type convergence the0- rems for semi-groups of linear operators of class (1, A) .Our results genaralize those of I. Miyadera [5] \S 0. Introduction The present paper deals with the problem of convergence of semigroups of linear operators, that is, determining wether or not a given sequence of semi-groups converge in some sense to a semi-group.This problem was investigated by many authors in the case of a sequence of C_{0}semi-groups T_{n}(t) satisfying the condition ||T_{n}(t)||\leq Me^{\omega t} n\in N ,