Journal of Operator Theory

Volume 94, Issue 2, Autumn 2025 pp. 457-472.

On the connectedness of the spectra of self-adjoint Toeplitz operators

Authors: Jingbo Xia (1), Congquan Yan (2)
Author institution: (1) College of Data Science, Jiaxing University, Jiaxing 314001, China and Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260, U.S.A.
(2) College of Data Science, Jiaxing University, Jiaxing 314001, China

Summary: We consider Toeplitz operators $T_f$ on the Hardy space $H^2(S)$ of the unit sphere $S$ in ${\mathbb C}^n$, $n \geqslant 2$. We show that if $f$ is a bounded, real-valued measurable function that depends only on $|z_1|, \dots ,|z_n|$, then the spectrum of $T_f$ is connected.

DOI: http://dx.doi.org/10.7900/jot.2023jan30.2465
Keywords: Toeplitz operator, spectrum

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