J. Korean Math. Soc. 2006; 43(4): 899-909
Printed July 1, 2006
Copyright © The Korean Mathematical Society.
Bhagwati P. Duggal, In Ho Jeon, and In Hyoun Kim
8 Redwood Grove Northfields Avenue, Seoul National University of Education, Seoul National University
Let $T$ be a bounded linear operator on a complex infinite dimensional Hilbert space $\mathscr{H}$. We say that $T$ is a quasi-class $A$ operator if $T^*|T^2|T\ge T^*|T|^2T$. In this paper we prove that if $T$ is a quasi-class $A$ operator and $f$ is a function analytic on a neighborhood of the spectrum of $T$, then $f(T)$ satisfies Weyl's theorem and $f(T^*)$ satisfies a-Weyl's theorem.
Keywords: quasi-class $A$ operators, Weyl's theorem, a-Weyl's theorem, a-Browder theorem
MSC numbers: Primary 47A53, 47B20
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