Criteria for toeplitz operators on the sphere

Jingbo Xia

doi:10.1090/S0002-9939-2012-11489-3

Criteria for toeplitz operators on the sphere

Jingbo Xia

Mathematics

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

Abstract

Let H²(S) be the Hardy space on the unit sphere S in Cⁿ. We show that a set of inner functions Λ is sufficient for the purpose of determining which A ∈ B(H²(S)) is a Toeplitz operator if and only if the multiplication operators {M_u: u ∈ Λ} on L²(S, dσ) generate the von Neumann algebra {M_f: f ∈ L^∞(S, dσ)}.

Original language	English
Pages (from-to)	637-644
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-2012-11489-3
State	Published - 2013

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title = "Criteria for toeplitz operators on the sphere",

abstract = "Let H2(S) be the Hardy space on the unit sphere S in Cn. We show that a set of inner functions Λ is sufficient for the purpose of determining which A ∈ B(H2(S)) is a Toeplitz operator if and only if the multiplication operators \{Mu: u ∈ Λ\} on L2(S, dσ) generate the von Neumann algebra \{Mf: f ∈ L∞(S, dσ)\}.",

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AB - Let H2(S) be the Hardy space on the unit sphere S in Cn. We show that a set of inner functions Λ is sufficient for the purpose of determining which A ∈ B(H2(S)) is a Toeplitz operator if and only if the multiplication operators {Mu: u ∈ Λ} on L2(S, dσ) generate the von Neumann algebra {Mf: f ∈ L∞(S, dσ)}.

UR - https://www.scopus.com/pages/publications/84870569216

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DO - 10.1090/S0002-9939-2012-11489-3

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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Criteria for toeplitz operators on the sphere

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