Let T be a bounded linear operator on a complex Hilbert space $mathfrak{H}$. An operator T is called class A operator if ${mid}T^2{mid}{geq}{mid}T{mid}^2$ and is called class $A({kappa})$ operator if $(T^*{mid}T{mid}^{2{kappa}}T)^{frac{1}{{kappa}+1}}{geq}{mid}T{mid}^2$ for a positive number ${kappa}$. In this paper, we show that ${sigma}$ is continuous when restricted to the set of class $A({kappa})$ operators.