Localization and the Toeplitz algebra on the Bergman space

DOI10.1016/j.jfa.2015.04.011zbMath1325.47065OpenAlexW2081769452MaRDI QIDQ2346105

Jingbo Xia

Publication date: 29 May 2015

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2015.04.011

zbMATH Keywords

Bergman spaceToeplitz operatorFock spacelocalizationseparated setToeplitz algebra

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Bergman spaces of functions in several complex variables (32A36) Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) (47L80)

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Translation-invariant operators in reproducing kernel Hilbert spaces ⋮ Essential normality for quotient modules and complex dimensions ⋮ Toeplitz and related operators on polyanalytic Fock spaces ⋮ A double commutant relation in the Calkin algebra on the Bergman space ⋮ The Berger-Coburn phenomenon for Hankel operators on the Fock space ⋮ Berger-Coburn Theorem, Localized Operators, and the Toeplitz Algebra ⋮ Essential commutants on strongly pseudo-convex domains ⋮ Algebras generated by Toeplitz operators on the unit sphere. II: Non commutative case ⋮ Hankel operators on weighted Bergman spaces and norm ideals ⋮ Toeplitz localization operators: spectral functions density ⋮ On the essential commutant of the Toeplitz algebra on the Bergman space ⋮ Radial operators on polyanalytic weighted Bergman spaces ⋮ Toeplitz operators associated with measures and the Dixmier trace on the Hardy space ⋮ Localization, Carleson measure and BMO Toeplitz operators on the Bergman space ⋮ On the localization of measure induced Toeplitz operators on the Bergman space ⋮ Correspondence theory on \(p\)-Fock spaces with applications to Toeplitz algebras ⋮ Band-dominated operators on Bergman-type spaces

Cites Work

• \(m\)-Berezin transform and compact operators
• Similarity of analytic Toeplitz operators on the Bergman spaces
• Localization and Berezin transform on the Fock space
• Density of algebras generated by Toeplitz operators on Bergman spaces
• Localization and compactness in Bergman and Fock spaces
• Toeplitz and Hankel operators and Dixmier traces on the unit ball of $\mathbb C^n$
• Heat Flow and Berezin-Toeplitz Estimates
• Approximation and then-Berezin transform of operators on the Bergman space
• The essential norm of operators in the Toeplitz algebra on $A^p(B_n)$
• Toeplitz operators and quantum mechanics
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