CONTINUITY OF THE SPECTRUM ON A CLASS A(k)

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