The Reduction Square Root and Perturbation for a Class of Strongly Continuous Operator Families

We introduce the concept of a times C-second resolvent families and present the rela- tionship between a times C-resolvent families and a times C-second resolvent families. Moreover, the perturbation and square root for a times C-resolvent families are considered in this paper which generalize the counterparts of C-Cosine operator functions.