Toeplitz Operators Associated with Measures and the Dixmier Trace on the Hardy Space

Liangying Jiang; Yi Wang; Jingbo Xia

doi:10.1007/s11785-020-00988-2

Toeplitz Operators Associated with Measures and the Dixmier Trace on the Hardy Space

Liangying Jiang
, Yi Wang
, Jingbo Xia

Mathematics

Shanghai Lixin University of Accounting and Finance
SUNY Buffalo

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

8 Scopus citations

Abstract

Let μ be a regular Borel measure on the open unit ball B in Cⁿ. By a natural formula, it gives rise to a Toeplitz operator T_μ on the Hardy space H²(S). We characterize the membership of Tμs, 0 < s≤ 1 , in any norm ideal C_Φ that satisfies condition (DQK). The same techniques allow us to compute the Dixmier trace of T_μ when Tμ∈C1+.

Original language	English
Article number	30
Journal	Complex Analysis and Operator Theory
Volume	14
Issue number	2
DOIs	https://doi.org/10.1007/s11785-020-00988-2
State	Published - Mar 1 2020

Keywords

Dixmier trace
Hardy space
Norm ideal
Toeplitz operator associated with measure

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10.1007/s11785-020-00988-2

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abstract = "Let μ be a regular Borel measure on the open unit ball B in Cn. By a natural formula, it gives rise to a Toeplitz operator Tμ on the Hardy space H2(S). We characterize the membership of Tμs, 0 < s≤ 1 , in any norm ideal CΦ that satisfies condition (DQK). The same techniques allow us to compute the Dixmier trace of Tμ when Tμ∈C1+.",

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AU - Xia, Jingbo

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Y1 - 2020/3/1

N2 - Let μ be a regular Borel measure on the open unit ball B in Cn. By a natural formula, it gives rise to a Toeplitz operator Tμ on the Hardy space H2(S). We characterize the membership of Tμs, 0 < s≤ 1 , in any norm ideal CΦ that satisfies condition (DQK). The same techniques allow us to compute the Dixmier trace of Tμ when Tμ∈C1+.

AB - Let μ be a regular Borel measure on the open unit ball B in Cn. By a natural formula, it gives rise to a Toeplitz operator Tμ on the Hardy space H2(S). We characterize the membership of Tμs, 0 < s≤ 1 , in any norm ideal CΦ that satisfies condition (DQK). The same techniques allow us to compute the Dixmier trace of Tμ when Tμ∈C1+.

KW - Dixmier trace

KW - Hardy space

KW - Norm ideal

KW - Toeplitz operator associated with measure

UR - https://www.scopus.com/pages/publications/85079823015

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JO - Complex Analysis and Operator Theory

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ER -

Toeplitz Operators Associated with Measures and the Dixmier Trace on the Hardy Space

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Keywords

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