Berger-Coburn Theorem, Localized Operators, and the Toeplitz Algebra

Publikation: Beitrag in Buch/Bericht/Sammelwerk/Konferenzband › Beitrag in Buch/Sammelwerk › Forschung › Peer-Review

Autoren

  • Wolfram Bauer
  • Robert Fulsche

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Details

OriginalspracheEnglisch
Titel des SammelwerksOperator Algebras, Toeplitz Operators and Related Topics
Herausgeber/-innenCham Birkhäuser
Herausgeber (Verlag)Springer Nature
Seiten53-77
Seitenumfang25
ISBN (elektronisch)9783030446512
ISBN (Print)9783030446505
PublikationsstatusVeröffentlicht - 2 Sept. 2020

Publikationsreihe

NameOperator Theory: Advances and Applications
Band279
ISSN (Print)0255-0156
ISSN (elektronisch)2296-4878

Abstract

We give a simplified proof of the Berger-Coburn theorem on the boundedness of Toeplitz operators and extend one part of this theorem to the setting of p-Fock spaces (1 ≤ p ≤∞). We present an overview of recent results by various authors on the compactness characterization via the Berezin transform for certain operators acting on the Fock space. Based on these results we present three new characterizations of the Toeplitz C* algebra generated by Toeplitz operators with bounded symbols.

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Berger-Coburn Theorem, Localized Operators, and the Toeplitz Algebra. / Bauer, Wolfram; Fulsche, Robert.
Operator Algebras, Toeplitz Operators and Related Topics. Hrsg. / Cham Birkhäuser. Springer Nature, 2020. S. 53-77 (Operator Theory: Advances and Applications; Band 279).

Publikation: Beitrag in Buch/Bericht/Sammelwerk/Konferenzband › Beitrag in Buch/Sammelwerk › Forschung › Peer-Review

Bauer, W & Fulsche, R 2020, Berger-Coburn Theorem, Localized Operators, and the Toeplitz Algebra. in C Birkhäuser (Hrsg.), Operator Algebras, Toeplitz Operators and Related Topics. Operator Theory: Advances and Applications, Bd. 279, Springer Nature, S. 53-77. https://doi.org/10.48550/arXiv.1905.12246, https://doi.org/10.1007/978-3-030-44651-2_8
Bauer, W., & Fulsche, R. (2020). Berger-Coburn Theorem, Localized Operators, and the Toeplitz Algebra. In C. Birkhäuser (Hrsg.), Operator Algebras, Toeplitz Operators and Related Topics (S. 53-77). (Operator Theory: Advances and Applications; Band 279). Springer Nature. https://doi.org/10.48550/arXiv.1905.12246, https://doi.org/10.1007/978-3-030-44651-2_8
Bauer W, Fulsche R. Berger-Coburn Theorem, Localized Operators, and the Toeplitz Algebra. in Birkhäuser C, Hrsg., Operator Algebras, Toeplitz Operators and Related Topics. Springer Nature. 2020. S. 53-77. (Operator Theory: Advances and Applications). doi: 10.48550/arXiv.1905.12246, 10.1007/978-3-030-44651-2_8
Bauer, Wolfram ; Fulsche, Robert. / Berger-Coburn Theorem, Localized Operators, and the Toeplitz Algebra. Operator Algebras, Toeplitz Operators and Related Topics. Hrsg. / Cham Birkhäuser. Springer Nature, 2020. S. 53-77 (Operator Theory: Advances and Applications).
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