CONTINUITY OF THE SPECTRUM ON A CLASS A(κ)

In Ho Jeon, In Hyoun Kim
2013 Korean Journal of Mathematics  
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 ) 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. t s+t ≥ |T * | 2t . Especially, we denote class A(1, 1) by class
doi:10.11568/kjm.2013.21.1.75 fatcat:oh3ypipgtrc47fi7ll5yon4zxi