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Commuting Toeplitz Operators and Hyperbolic Geometry

Part of the Operator Theory: Advances and Applications book series (OT, volume 185)

Abstract

The C*-algebras of Toeplitz operators considered in Chapters 5, 6, and 7 are commutative. This property is impossible (except for the trivial case of scalar operators ≡ constant defining symbols) for the C*-algebras of Toeplitz operators acting on the Hardy space. The special features of the defining symbols which make this phenomenon possible were symbols depending only on the imaginary part of a variable for Toeplitz operators on the upper half-plane, radial symbols for Toeplitz operators on the unit disk, and symbols depending only on the angular part of a variable for Toeplitz operators on the upper half-plane, respectively. In this stage a natural question appears: whether there exist other classes of defining symbols which generate commutative Toeplitz operator C * -algebras, and how they can be classfied.

Keywords

Unit Disk Toeplitz Operator Hyperbolic Geometry Weighted Bergman Space Bergman Kernel Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2008

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