Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON WEYL'S THEOREM FOR QUASI-CLASS A OPERATORS

  • Duggal Bhagwati P. (8 Redwood Grove Northfields Avenue) ;
  • Jeon, In-Ho (Department of Mathematics Education Seoul National University of Education) ;
  • Kim, In-Hyoun (Department of Mathematics Seoul National University)
  • Published : 2006.07.01
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Abstract

Let T be a bounded linear operator on a complex infinite dimensional Hilbert space $\scr{H}$. We say that T is a quasi-class A operator if $T^*\|T^2\|T{\geq}T^*\|T\|^2T$. In this paper we prove that if T is a quasi-class A operator and f is a function analytic on a neigh-borhood or the spectrum or T, then f(T) satisfies Weyl's theorem and f($T^*$) satisfies a-Weyl's theorem.

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