In this paper, the mixed and ordinary operators are characterized in the classes of r̂ -set, r̂ -set, ????̂∗-set and ????̂∗-set. More over the behavior of r̂ -set, r̂ - set, ????̂∗-set and ????̂∗-set in spaces are investigated. The Inclusion chains among the mixed and ordinary operators are refined in the domains of r̂ -set, r̂ -set, ????̂∗-set and ????̂∗-set