CONTINUITY OF THE SPECTRUM ON A CLASS A(κ)

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.