ON THE CONNECTEDNESS OF THE SPECTRA OF SELF-ADJOINT TOEPLITZ OPERATORS

Jingbo Xia; Congquan Yan

doi:10.7900/jot.2023jan30.2465

ON THE CONNECTEDNESS OF THE SPECTRA OF SELF-ADJOINT TOEPLITZ OPERATORS

Jingbo Xia
, Congquan Yan

Mathematics

Jiaxing University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider Toeplitz operators T_f on the Hardy space H²(S) of the unit sphere S in Cⁿ, n≥ 2. We show that if f is a bounded, real-valued measurable function that depends only on |z₁|, . . ., |z_n|, then the spectrum of T_f is connected.

Original language	English
Pages (from-to)	457-472
Number of pages	16
Journal	Journal of Operator Theory
Volume	94
Issue number	2
DOIs	https://doi.org/10.7900/jot.2023jan30.2465
State	Published - Sep 2025

Keywords

Toeplitz operator, spectrum

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10.7900/jot.2023jan30.2465

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title = "ON THE CONNECTEDNESS OF THE SPECTRA OF SELF-ADJOINT TOEPLITZ OPERATORS",

abstract = "We consider Toeplitz operators Tf on the Hardy space H2(S) of the unit sphere S in Cn, n≥ 2. We show that if f is a bounded, real-valued measurable function that depends only on |z1|, . . ., |zn|, then the spectrum of Tf is connected.",

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N2 - We consider Toeplitz operators Tf on the Hardy space H2(S) of the unit sphere S in Cn, n≥ 2. We show that if f is a bounded, real-valued measurable function that depends only on |z1|, . . ., |zn|, then the spectrum of Tf is connected.

AB - We consider Toeplitz operators Tf on the Hardy space H2(S) of the unit sphere S in Cn, n≥ 2. We show that if f is a bounded, real-valued measurable function that depends only on |z1|, . . ., |zn|, then the spectrum of Tf is connected.

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ON THE CONNECTEDNESS OF THE SPECTRA OF SELF-ADJOINT TOEPLITZ OPERATORS

Abstract

Keywords

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