Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2006; 43(4): 899-909

Printed July 1, 2006

Copyright © The Korean Mathematical Society.

On Weyl's theorem for quasi-class $A$ operators

Bhagwati P. Duggal, In Ho Jeon, and In Hyoun Kim

8 Redwood Grove Northfields Avenue, Seoul National University of Education, Seoul National University

Abstract

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