Semi-Quasitriangularity of Toeplitz Operators with Quasicontinuous Symbols
Commun. Korean Math. Soc. 1998 Vol. 13, No. 1, 77-84
In Hyoun Kim, Woo Young Lee
Sung Kyun Kwan University, Sung Kyun Kwan University
Abstract : In this note we show that if $T_\varphi$ is a Toeplitz operator with quasicontinuous symbol $\varphi$, if $\Omega$ is an open set containing the spectrum $\sigma(T_{\varphi})$, and if $H(\Omega)$ denotes the set of analytic functions defined on $\Omega$, then the following statements are equivalent: \roster \item"(a)" $T_\varphi$ is semi-quasitriangular. \item"(b)" Browder's theorem holds for $f(T_\varphi)$ for every $f\in H(\Omega)$. \item"(c)" Weyl's theorem holds for $f(T_\varphi)$ for every $f\in H(\Omega)$. \item"(d)" $\sigma(T_{f\circ \varphi})=f(\sigma(T_\varphi))$ for every $f\in H(\Omega)$.
Keywords : Toeplitz operators, quasicontinuous functions, semi-quasi- triangular, Weyl's theorem, Browder's theorem
MSC numbers : 47B35, 47A10
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