A generalization of sectorial and quasi-sectorial operators

In the paper we generalize the main results presented in Bentkus and Paulauskas (2004) [2] by giving rates of approximation of some semigroups of operators of the order n−α, 0 < α 1. Also two classes of operators, generalizing sectorial and quasi-sectorial operators, are introduced and their properties are studied. © 2011 Elsevier Inc. All rights reserved