Toeplitz operators in Bergman space induced by radial measures

Fuente: arXiv
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Main Authors: Maximenko, Egor A., Pacheco, Carlos G.
Format: Preprint
Published: 2025
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author Maximenko, Egor A.
Pacheco, Carlos G.
author_facet Maximenko, Egor A.
Pacheco, Carlos G.
contents We study radial Carleson--Bergman measures on the unit disk and the corresponding Toeplitz operators acting in the Bergman space. First, we show that such Toeplitz operators are diagonal in the canonical basis, and we compute their eigenvalue sequences and Berezin transforms in terms of the radial component of the measure. Next, considering the average values of radial measures near the boundary, we give a simple characterization of radial Carleson--Bergman measures. Finally, we prove that the eigenvalue sequences of such Toeplitz operators are Lipschitz continuous with respect to the logarithmic distance on natural numbers. As a consequence, we describe the commutative C*-algebra generated by Toeplitz operators induced by radial Carleson--Bergman measures.
format Preprint
id arxiv_https___arxiv_org_abs_2503_23649
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Toeplitz operators in Bergman space induced by radial measures
Maximenko, Egor A.
Pacheco, Carlos G.
Functional Analysis
Operator Algebras
Primary 47B35, Secondary 32A36, 28C10, 44A60
We study radial Carleson--Bergman measures on the unit disk and the corresponding Toeplitz operators acting in the Bergman space. First, we show that such Toeplitz operators are diagonal in the canonical basis, and we compute their eigenvalue sequences and Berezin transforms in terms of the radial component of the measure. Next, considering the average values of radial measures near the boundary, we give a simple characterization of radial Carleson--Bergman measures. Finally, we prove that the eigenvalue sequences of such Toeplitz operators are Lipschitz continuous with respect to the logarithmic distance on natural numbers. As a consequence, we describe the commutative C*-algebra generated by Toeplitz operators induced by radial Carleson--Bergman measures.
title Toeplitz operators in Bergman space induced by radial measures
topic Functional Analysis
Operator Algebras
Primary 47B35, Secondary 32A36, 28C10, 44A60
url https://arxiv.org/abs/2503.23649