DOI: https://doi.org/10.11568/kjm.2013.21.1.75

### CONTINUITY OF THE SPECTRUM ON A CLASS A(k)

#### Abstract

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.

#### Subject classification

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ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr